One of the vertices of △PQR is P(2, −1). The midpoint of PQ is M(3, 0). The midpoint of QR is N(5, 3). Show that MN || PR and MN = 1/2 PR.

The coordinates of Q are:

The coordinates of R are:

The slope of MN is:

The slope of PR is:

The line segments are (select)

MN =

PR =

Answers

Answer 1

Answer:

See the proof below

Step-by-step explanation:

Given the following coordinates

P(2, −1)

Midpoint of PQ M(3, 0)

We can get the coordinate point Q using the midpoint formula;

M(X,Y) = (x1+x2/2, y1+y2/2)

X = x1+x2/2

3 = 2+x2/2

6 = 2+x2

x2 = 6-2

x2 = 4

Y = y1+y2/2

0 = -1+y2/2

0 = -1 + y2

y2 = 0+1

y2 = 1

Hence the coordinate of Q is (4, 1)

Next is to get the coordinate of R

Given the midpoint of QR to be N(5, 3)

(5,3) = (4+x2/2, 1+y2/2)

5 = 4+x2/2

10 = 4+x2

x2 = 10-4

x2 = 6

1+y2/2 = 3

1+y2 = 6

y2 = 6-1

y2 = 5

Hence the coordinate of R is (6,5)

Given the coordinates M(3, 0) and N(5, 3)

Slope is expressed as:

m = y2-y1/x2-x1

m = 3-0/5-3

m = 3/2

Slope of MN = 3/2

Get the slope of PR

Given the coordinates P(2, −1) and R (6,5)

Slope of PR = 5-(-1)/6-2

Slope of PR = 5+1/4

Slope of PR = 6/4 = 3/2

Since the slope of MN is equal to that of PR, hence MN is parallel to PR i.e MN || PR

To show that MN = 1/2PR, we will have to take the distance between M and N and also P and R first as shown:

For MN with coordinates  M(3, 0) and N(5, 3)

MN = √(x2-x1)²+(y2-y1)²

MN = √(5-3)²+(3-0)²

MN = √2²+3²

MN = √13

Get the length of PR where P(2, −1) and R (6,5)

PR = √(6-2)²+(5+1)²

PR = √4²+6²

PR = √16+36

PR = √52

PR = √4*13

PR = √4*√13

PR = 2√13

Since MN = √13

PR = 2MN

Divide both sides by 2

PR/2 = 2MN/2

PR/2 = MN

Hence MN = 1/2 PR (Proved!)


Related Questions

Usually Holly leaves home to school at 9:00, however today she left home 20 minutes later. In order to be at school on time she increased her usual speed by 20% and still was at school 15 minutes later than usual. What is her usual time from home to school

Answers

Answer:

Her usual time from home to school is 30 minutes

Step-by-step explanation:

At any point in time;

distance = speed * time

Here, we want to calculate the normal time she spent going from home to school

Let the normal time be x minutes

And the normal speed be t m/min

Today, she increased her speed by 20%

Her speed today will be t + 20/100 * t =

1.2t m/min

Her distance from how to school normally is

xt meters

Now what this means is that, at the increased speed, she was able to get to school 5 minutes earlier

What we are saying is although, she lost 20 minutes initially, she was able to beat down the lateness by 5 minutes

So, the time spent on her increased speed journey is;

(x-5) minutes

At any point in time, the distance will be equal;

Thus, mathematically;

xt = 1.2t(x-5)

xt = 1.2xt - 6t

6t = 1.2xt-xt

6t = 0.2xt

t cancels out

0.2x = 6

x = 6/0.2

x = 30 minutes

I need help with this

Answers

Answer:

x = 24.52

Step-by-step explanation:

Since this is a right triangle, use Pythagorean Theorem to solve for the hypotenuse.

Pythagorean Theorem: a² + b² = c²

24² + 5² = x²

576 + 25 = x²

601 = x²

√601 = x

An air conditioning system can circulate 420 cubic feet of air per minute. How many cubic yards of air can it circulate per​ minute?

Answers

Answer:

15.5556 cubic yards

Step-by-step explanation:

A yard is equal to three feet.  Divide the volume value by 27 (3 cubed).

Latoya can plant 1/3of her garden in 2/5 hour. If she continues working at this rate, what fraction of Latoya’s garden can she plant in one hour?

Answers

Answer:

Latoya can plant 5/6 of her garden in one hour.

Step-by-step explanation:

☆We can solve using proportion!

[tex] \frac{ \frac{1}{3 } \: of \: garden }{ \frac{2}{5} \: of \: hour } = \frac{x}{1 \: hour} \\ \\ \frac{ \: \frac { 2}{5}x }{ \frac{2}{5} } = \frac{ \frac{1}{3} }{ \frac{2}{5} } \\ \\ x = \frac{5}{6} [/tex]

H/7 =27 can some one answer this pls

Answers

Answer:

h=189

Step-by-step explanation:

solve for H by simplifying both sides of the equation, then isolating the variable.

hope this helped

The distance between -18 and 15 is equal to ______.
A. 18 - 15
B. 15 - 18
C. -18 - 15
D. 15 - (-18)

Answers

Answer:

It would be equal to 15 - (18)

Answer:

it would actually be (B)

PLEASE HELP its multiple choice i’ll mark brainliest and i added a couple points

Answers

Answer:

i think it the third one but i don't know i'm not in collage math class so...

Step-by-step explanation:


Which statement illustrates the commutative property of addition?
A. (8i + 4) + (-8i – 4) = 0
B. (8i)- (-8i)= 0
C. 8i + 4 = 4i + 8
D. 8i + 4 = 4 + 8i

Answers

Answer:D

Step-by-step explanation:its the same thing but the numbers are flipped, you get the same answer either way.

The statement that illustrates the commutative property of addition is

8i + 4 = 4 + 8i. The correct option is D.

What is the commutative property of addition?

The commutative property of addition:

Let a and b are numbers.

a + b =  b + a

The change in the position of two numbers in an addition operation does not change the sum.

The commutative property of addition:

Let a and b are numbers.

So, a + b =  b + a.

LHS = 8i + 4

= 2 (4i+2)

= 2(2 + 4i)

=  4 + 8i

That means,  8i + 4 = 4 + 8i holds the commutative property of addition.

Therefore, the equation is 8i + 4 = 4 + 8i.

To learn more about the commutative property;

https://brainly.com/question/778086

#SPJ2

3. There are 2 girls and 3 boys on a camping trip. What is the ratio of girls to boys on the trip? Choose all that apply. 2:3 2 to 5 2:5 2 to 3

Answers

Answer:

2:3

Step-by-step explanation:

5 in total as you subtract the dudes

Several members of a running club would like to survey the rest of the members to determine which 5K races the club should enter. They decide to use a random number table to sample 10 of the 78 members. Which of the following correctly labels the population?

A.) 0–78
B.) 1–78
C.) 00–78
D.) 01–78

Answers

Answer:

D

Step-by-step explanation: edge 2021

1490 thousand help me get that number because I can't find them

Answers

Answer:

1,490,000

Step-by-step explanation:

Answer:

1490000?

Step-by-step explanation:

What is the slope of the linear function
graphed below?

Answers

Answer: C

Step-by-step explanation:

Please answer this correctly without making mistakes I want ace expert and genius people to answer this correctly without making mistakes

Answers

Answer:

6936 pints and 1156 cups

Step-by-step explanation:

Answer:

7514 pints

Step-by-step explanation:

i rechecked and this was correct?

Select all of the solutions to the equation below.



12x2=24




−23–√


23–√


−2–√


2–√


−2


2

Answers

Answer:

12 x 2+23 x −24=0. Enter an equation ... The first term is, 12x2 its coefficient is 12 . ... B ± √ B2-4AC x = ———————— 2A In our case, A = 12. B = 23. C = -24

Step-by-step explanation:

12 x 2+23 x −24=0. Enter an equation ... The first term is, 12x2 its coefficient is 12 . ... B ± √ B2-4AC x = ———————— 2A In our case, A = 12. B = 23. C = -24

hi can you tell me whether a appeal must be filed within 6 months of a claim determination. its medical billing chapter 18​

Answers

Answer: Decisions and Determinations -If a Medicare appeal request does not result in a dismissal, adjudication of ... dismissal by providing an explanation for the late filing to the MAC within 6 months of the dismissal of the.

Step-by-step explanation:g brain

I don't understand can someone help me PLZ

Answers

The answer is 1/2. Count how many a out of the total.

Answer:

1/2

Step-by-step explanation:

the circle has 8 pieces so that's how you get the denominator

you count how many A's there are and that is your numerator

so now 4/8 and reduce to get a half

Please help. I dont understand how to do this. Enter the coordinates of the vertices of (Ry-axis ∘ r(90°, O))(QRST).

Answers

Answer:

I think it's

Q = ( 1 , 3 )

R = ( 3 , 3 )

S = ( 0 , 2 )

T = ( -2 , 1 )

Step-by-step explanation:

please tell me if this is wrong.

Hope this helps!

The question is:
Which calculation and answer show how to convert 13/16 into a decimal

Answers

Answer:

I think the answer is D

Step-by-step explanation:

Answer is D, because if you divide 13 and 15 it gives you 0.8125

3/8 × 4/11 =
three eighths times four elevenths

Answers

Answer:

12/88, which is 3/22 in simplest form.

Answer:

12/88 Simplified:3/22

Step-by-step explanation:

you just multiply the numerator but the numerator and then denominator but the denominator. Then you just simplify

Hope that helps:)

A mother otter spends 1/3 of each day feeding her baby. How many hours does the mother otter spend feeding her baby in 1​ week?

Answers

56

1/3 of 24 (hrs) is 7.999 (rounded to 8)
and multiply 7 (days out of the week) by the hrs

The waiting time for a bus has a uniform distribution between 2 and 13 minutes. What is the probability that the waiting time for this bus is less than 4.5 minutes on a given day

Answers

Answer: 0.2273

Step-by-step explanation:

Probability density function for uniform distribution is given by :-

[tex]f(x)=\dfrac{1}{b-a}[/tex], where x is uniformly distributed in [a,b].

Let x denotes the waiting time for this bus.

Given : The waiting time for a bus has a uniform distribution between 2 and 13 minutes.

Probability distribution function of x for interval [2,13] will be :-

[tex]f(x)=\dfrac1{13-2}=\dfrac{1}{11}[/tex]

Required probability : P(x<4.5) = [tex]\int^{4.5}_{2}f(x)\ dx[/tex]

[tex]=\int^{4.5}_{2}\dfrac1{11}\ dx\\\\=\dfrac1{11}[x]^{4.5}_{2}\\\\ = \dfrac1{11}(4.5-2)\\\\=\dfrac1{11}(2.5)\approx0.2273[/tex]

Hence, the probability that the waiting time for this bus is less than 4.5 minutes on a given day = 0.2273

What is the slope of a line parallel to y=2x + 3

Answers

Answer:

2

Step-by-step explanation:

The slope of the line with equation y=2x+3 is 2 . So, any line parallel to y=2x+3 has the same slope 2 .

Hello!

Parallel lines have the same slope. So if one line has a slope of 2, the line parallel to it has a slope of 2 as well.

Therefore, the slope is 2. Hope it helps.

If you have any questions, feel free to ask.

~A forlorn teen

[tex]MagicalNature[/tex]

The graph below shows the solution to which system of inequalities?

Answers

D is the answer to the problem

PLZZ HELPP ILL GIVE BRAINLIST

Answers

it’s green:b purple:d blue:c red:a because

Simplify
2g + 4h + 4i -8g + 3h - 4i​

Answers

Answer:

-6g + 7h

Step-by-step explanation:

A company wants to test clear deck sealants for weather resistance. Three brands of sealants will be tested using 60 pieces of decking wood. The company wants to create treatment groups of 20 pieces of wood each, and decide to randomize using slips of paper. Select all the approaches that would result in comparable treatment groups. The numbers 1, 2, and 3 are each written on 20 slips of paper, and the slips are placed in a hat and shaken well. The top piece of wood from a stack is selected and a slip of paper is drawn from the hat. That piece of wood is assigned to the group number on the slip. The slip of paper is returned to the hat. This continues until all pieces of wood have been assigned to a group. The numbers 1, 2, and 3 are written on three slips of paper, put into a hat, and shaken well. A slip is drawn and the first 20 pieces of wood on the stack are assigned to the group number on the slip. Another slip is drawn and the next 20 pieces of wood are assigned to that group. The remaining pieces of wood are assigned to the remaining group. Each piece of decking wood is assigned a number from 1 to 60. The numbers 1–60 are written on slips of paper and placed in a hat and shaken well. Twenty slips are drawn, shaking the hat after each slip of paper is drawn, and the pieces of wood corresponding to those numbers are placed in group 1. Twenty more slips are drawn in the same way, and the pieces of wood corresponding to those numbers are placed in group 2. The pieces of wood corresponding to the numbers on the remaining slips are placed in group 3. The numbers 1, 2, and 3 are each written on 20 slips of paper (20 for each number) and the slips are placed in a hat and shaken well. The top piece of wood from a stack is selected, and a slip of paper is drawn from the hat. That piece of wood is assigned to the group number on the slip. The slip of paper is not returned to the hat. This continues until all pieces of wood have been assigned to a group.

Answers

Answer:

The Answer is C and D

Step-by-step explanation:

Just did it

One card is selected at random from a deck of cards. Determine the probability that the card selected is a card greater than 3 and less than 8.

Answers

Answer:

4/13

Step-by-step explanation:

Count all cards that are 4, 5, 6, and 7 (each of 4 different suits) so the number of cards that is greater than 3 and less than 8 = 4(4) = 16.

There are 52 cards in a standard deck of cards.

P(greater than 3 and less than 8)

= 16/52

= 4/13

turn -2x+4y=0 into slope-intercept form

Answers

Y=1/2x +0. You add the 2x to the other side, and then divide everything by 4 to have only 1y.

A local animal rescue group received a number of $10 donations (D) for its annual drive. Suppose the total of the donations (T) reached $930. Which equations apply to this situation?

Answers

930/10 = number of donations

Answer:

&80/yt5

Step-by-step explanation:

E

a piece of cheese weighting 2/3 pound is to be divided into 8 equal portions. what will be the weight of each portion?

Answers

Answer:

1/12 lb

Step-by-step explanation:

2/3 x 1/8 = 2/24 = 1/12

Answer: 1/12

Step-by-step explanation: 2/3 / 8/1 is actually multiplying the first number by the reciprocal of the second. So 2/3 x 1/8. That equals 0.08333... or 1/12.

Hope this helps!

Other Questions
What factors led to western expansion from 1800-1850?Submit calculate the mass of a sample of cobalt containing 3.31x10^22 atoms Which transition would be BEST to add at the beginning of paragraph 2?wA)HoweverB)Otherwise0)As a resultD)In the future 20. Analyzing the map above, which physical geographic feature influenced where themissions and presidios were built in Texas?F. mountainsG. citiesH. riversJ. heavy rainfall A scale model of an object is 6 inches tall. The actual object is 324 feet tall. What is the scale factor of the model Why Am I Different From Everyone Else Around Me in a school, 56% of the 850 students are girls. work out the number of girls in the school i realy need help with this: 2 2/3 divided by 9 Why does the party run into problems in Mirkwood?Question 3 options:Gandalf deceives them.Bilbo and the dwarves do not follow Beorn's advice.The dwarves do not think before they act.The elves and the spiders attack Bilbo and the dwarves while they sleep Help me please. There will be the one choice on one of them Taking a recipe and breaking it down into its individual sections, like ingredients, preparation, cooking instructions, and nutritional information, is an example of _____.refinementpattern recognitiondecompositionabstraction What factors led to the golden age? should members of the black community carry guns to protect against police brutality today? 4j = 0.7 Solve for j Read the excerpt from "The Monkey's Paw."It had a spell put on it by an old fakir," said the sergeant-major, "a very holy man. He wanted to show that fate ruled people's lives, and that those who interfered with it did so to their sorrow. He put a spell on it so that three separate men could each have three wishes from it."His manner was so impressive that his hearers were conscious that their light laughter jarred somewhat."Well, why don't you have three, sir?" said Herbert White, cleverly.The soldier regarded him in the way that middle age is wont to regard presumptuous youth. "I have," he said, quietly, and his blotchy face whitened."And did you really have the three wishes granted?" asked Mrs. White."I did," said the sergeant-major, and his glass tapped against his strong teeth."And has anybody else wished?" persisted the old lady."The first man had his three wishes. Yes," was the reply; "I don't know what the first two were, but the third was for death. That's how I got the paw."Which event does the excerpt foreshadow?A. the sergeant-major's return to India and the resulting tragedyB. the sergeant-major obtaining the paw and the resulting tragedyC. Mr. White's refusal of the paw and the resulting tragedyD. Mr. White accepting the paw and the resulting tragedy Find the perimeter in simplest form and explain your work Do you think an organism can survive alone in nature. justify your view. Driving 65 mph, it takes Alicia 3 hours to reach the airport to go on a vacation. It then takes her 4 hours to get to her destination with the jet traveling at a speed of 450 mph. How many miles does Alicia travel to get to her destination? songs for when i'm in my feeling NEED HELP QUICK! WILL GIVE BRAINLIESTQuoting Relevant Information (Part 1)