Given the vertices of a triangle ABC below, find the midpoint and length of the midsegment. Give your length in simplified radical form.

Given The Vertices Of A Triangle ABC Below, Find The Midpoint And Length Of The Midsegment. Give Your

Answers

Answer 1

Answer:

Midpoint of AC = (-1, 1)

Midpoint of BC = (1, -2)

Length of the midsegment = [tex]\sqrt{13}[/tex]

Step-by-step explanation:

Vertices of a triangle ABC are A(0, 5), B(4, -1) and C(-2, -3).

Midpoint of segment AC = [tex]\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]

                                         = [tex](\frac{0-2}{2},\frac{5-3}{2})[/tex]

                                         = (-1, 1)

Midpoint of BC = [tex](\frac{4-2}{2},\frac{-1-3}{2})[/tex]

                         = [tex](1,-2)[/tex]

Length of the mid segment = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                                              = [tex]\sqrt{(-1-1)^2+(-2-1)^2}[/tex]

                                              = [tex]\sqrt{4+9}[/tex]

                                              = [tex]\sqrt{13}[/tex]


Related Questions

Without graphing, determine whether the system of linear equations has one solution, infinitely many solutions, or no solution. Explain your reasoning.

[tex]y=15x+1[/tex]
[tex]y=15x+2[/tex]

Answers

[tex]\huge{ \mathcal{  \underline{ Answer} \:  \:  ✓ }}[/tex]

First equation :

[tex]y = 15x + 1[/tex]

[tex]y - 15x - 1 = 0[/tex]

Second equation :

[tex]y = 15x + 2[/tex]

[tex]y - 15x - 2 = 0[/tex]

Now, the equations are in the form of

[tex]a_1x {}^{2} + b_1x + c_1 = 0[/tex]

[tex]a_2x {}^{2} + b_2x + c_2 = 0[/tex]

where,

[tex] \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2} [/tex]

therefore the equations would have no solution .

_____________________________

[tex]\mathrm{ \#TeeNForeveR}[/tex]

Ryan has 10 quarters.
Kelly has exactly seven times as much money as Ryan.
They will combine their money to buy a game.
The game costs $27. How much more money do they need to
save?

Answers

Answer:

its b

Step-by-step explanation:

What is the value of the expression 6x - y when x = 3 and y = 1? (5 points)
012
8
O 3
d
17

Answers

Answer:

the answer is 17

Step-by-step explanation:

6×3-1

= 17

A bakery sells ten different types of bread. The amount of cups of sugar in each bread

recipe is shown.

1

2

1

4

4

3

4

ili i

13

1

2

1

2

What is the mean amount of sugar in these recipes?

Answers

Answer:

3/4 cups

Step-by-step explanation:

Adding the fractions

1/4 + 1/2 + 1/4 + 3/4 + 1 + 1 1/2 + 1/2 + 1 3/4 + 1/2 + 1/2

And the the L.C.M to be 4

=30/4

=15/2

Mean = 15/2 ÷ 10

=15/2 × 1/10

3/4

Someone please help me thank you

Answers

Answer:

[tex]y=-\frac{1}{3}x+-7[/tex]

Step-by-step explanation:

The graph shows a negative slope with 3 units in between each point.

Every 3 x-units, the y-unit goes up once.

1.
40cm
40cm
85cm
Can a one metre rod fit inside of the box?
Explain your answer

Answers

Answer:

donknow

Step-by-step explanation:

help fr now i am in danger x_x

Answers

Answer:

B, it's a reflection over the y-axis

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

It's B because all your doing is flipping the image over the y-axis

I don’t understand how to do this . Any help would be appreciated thank you .

Answers

(B)

Step-by-step explanation:

Look at the triangle with the 65° angle. Note that the 65° angle is opposite the 24-ft side and p is the length of the triangle's hypotenuse so let's use the definition of sine 65°:

sin 65 = opposite/hypotenuse

= (24 ft)/p

Solving for p,

p = (24 ft)/(sin 65°)

= 26.48 ft

Emily is buying new cold-weather gear for her family. She pays $100 for 5 pairs of waterproof gloves that each cost the same amount. Four of the pairs of gloves are mittens. Which expression represents the total cost of the 4 pairs of mittens?​

Answers

5÷100=x

x=20

100-20=80

80= the total cost of the 4 pairs of mittens

5x=100
X=20
4x=80
This should be the expression

12
Which number sentence is true?
A
B.
4y2 + 2 = (4y x 4y) + 2
4y2 + 2 = (4y + y) + 2
4y2 + 2 = 4(y + y) + 2
4y? + 2 = 4(y x y) + 2
с
D

Answers

Answer:

D - 4(y x y) + 2

Step-by-step explanation:

(y x y) + y2

4 x y2 = 4y2

which gives you 4y2 + 2

D is the answer hope this helps

please find the vertex to this quadratic

Answers

Is = 2 ………………………………..,…..

hey! i’ll give brainliest please help

Answers

Answer:

I think it's D

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

They are anxious to get their results

factorise completely

a). 3xy - 9x

b). x² - 4

c). 2x² + 5y + 1​

Answers

Answer:

a) 3x(y-3)

b) (x-2)(X+2)

Step-by-step explanation:

See the steps below:) You can also use the app photo math, you take a picture and it will give you the answer and explain the steps:)

what is 713.49 written in standard form?

Answers

Answer:     Seven hundred thirteen point forty-nine.

Step-by-step explanation:    Hope this helps ;)

What is the least common denominator of the equation 2/9x + 2/3x =7 ?

Answers

Answer:

that would be 9 as the least common denominator

Step-by-step explanation:

Simplify and give me steps please.
(5m^4/3 x 5n^1/4) (m^1/3 x 2n^1/8)

Answers

Answer:

(25m^4n^1/12)(m^1n^1/12)

Step-by-step explanation:

Re-order terms to the left.  

(5*5m^4/3 * n^1/4) (m^1/3*2n^1/8)

Combine terms

(5*5m^4n^1/3/4)     2m^1n^1/3/3/8    

Multiply

(25m^4n^1/3/4)       2m^1n^1/3/3/8    

(25m^4n^1/3 * 4)    2m^1n^1/3/3*8    

(25m^4n^1/12).        2m^1n^1/3/24

cancel common terms in both num and denominator

   

Final - (25m^4n^1/12) (2m^1n^1/12).

The city is planting new trees in its downtown to make the streets more comfortable for visitors.They are planting each tree 12 feet apart.How many trees can they plant on 2 miles of streets? 5280 feet = 1 mile.

Answers

880 trees 5280•2/12=880

What is the slope, m, and the y-intercept of the line that is graphed below?

Answers

Answer:

m=1 (0,3)

Step-by-step explanation:

m=1

slope is 1 because from left to right the line goes up and you move one 1and one to the left so m=1/1 =1

y-intercept is at (0,3) because is where the line intersects the y-axis

Jaxon is flying a kite, holding his hands a distance of 2.5 feet above the ground and
letting all the kite's string play out. He measures the angle of elevation from his hand
to the kite to be 33. If the string from the kite to his hand is 150 feet long, how many
feet is the kite above the ground? Round your answer to the nearest hundredth of a
foot if necessary

Answers

Answer:

Step-by-step explanation:

As Jaxon holding his hands a distance of 2.5 feet above the ground.

means h1= 2.5 feet

elevation angle from the hand is 33° so ∅=33°

distance of kite from his hand is  150 feet

so from the image we can see , now

as we know that  ,

Sin∅ =h2/150

Sin33°=h2/150

0.55 =h2/150                   (Sin33°= 0.545)

so h2= 81.70 feet

so height from ground is (H)=h1+h2= 2.5+81.70

H=84.20 feet

which type of parent function is f(x) = 3^x?

Answers

Answer:

c

Step-by-step explanation:

because there is a 3 in front of the root it is a cubed root since

2= square- the two is invisible but its there

3= cubed

C



HOPE THIS HELPS!! Have a nice day

Marking brainliest

Please help!

Answers

Answer:

[tex]AB\approx 24.22[/tex]

Step-by-step explanation:

In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse of the triangle.

In this case, in order to form the ratio, we're looking for the angle to the bottom right of the triangle. Notice how this angle is the supplement to the angle marked [tex]130.8^{\circ}[/tex]. Since the two angles form one side of the line, we can solve for this angle.

Let's call the angle [tex]\theta[/tex]:

[tex]130.8+\theta=180,\\\theta=49.2^{\circ}[/tex]

From basic. trig for right triangles (refer to first paragraph in answer):

[tex]\sin 49.2^{\circ}=\frac{AB}{32},\\AB=32\sin 49.2^{\circ}=24.2238417809\approx \boxed{24.22}[/tex]

ok y’all i need to know something.
today is the last day of school and my grades are all a’s and b’s but i have a few projects i didn’t do. will i still pass the school year?

Answers

Yes it won’t drop your grade too much and you’ll pass <3

Answer:

you will still pass

Step-by-step explanation:

your grades might drop a little

2,668 ÷ 53 (Im putting this because it has to be 20 characters or more)

Answers

Answer:

50.33962264

Step-by-step explanation:

brainlest pls

Answer:

the answer is 50.33

Step-by-step explanation:

someone check out my recent question

Please help! Choose 2 statements that are true

Answers

Answer:

I think it's C and E am not sure

please help meeee. Pleaseeee

Answers

Answer:

in excact terms: 50.26548

to the nearest tenth: 50.3

Step-by-step explanation:

Answer:

Step-by-step explanation:

V = radius^2  x height x π = 4^2 x 1 x π = 16π in^3

16 x 3.14 = 50.26...  = 50.3 in^3

Suki rode her bike 6/7 mile. Claire rode her bike 1/3 mile. They want to compare how far they each rode their bikes using benchmark 1/2. Select the correct answer to describe how to solve the problem.

Answers

Answer:

6/7 > 1/2

1/3 < 1/2

Suki rode her bike a longer distance than Clarie

Step-by-step explanation:

Suki's distance = 6/7 miles

Compare with bechmark 1/2

6/7 and 1/2

Make the denominators same

(6*2)/(7*2) and (1*7)/(2*7)

12/14 and 7/14

12/14 is greater than 7/14

12/14 > 7/14

Therefore, 6/7 > 1/2

Clarie distance = 1/3 miles

Compare with bechmark 1/2

1/3 and 1/2

Make the denominators same

(1*2)/(3*2) and (1*3)/(2*3)

2/6 and 3/6

2/6 is less than 3/6

2/6 < 3/6

Therefore,

1/3 < 1/2

Compare Suki's distance with Clarie

compare 6/7 and 1/3

Make the denominators same

(6 * 3)/(7 * 3) and (1 * 7)/(3 * 7)

18/21 and 7/21

18/21 > 7/21

Suki rode her bike a longer distance than Clarie

What is the value of the expression? (14 ½ - 10.25) ÷ 2

Answers

Answer:

[tex](14 \frac{1}{2} - 10.25) \div 2 \\ = ( \frac{29}{2} - 10.25) \div 2 \\ = 4.25 \div 2 \\ = 2.125 \\ = 2 \frac{1}{8} [/tex]

answer this question

Answers

pretty sure it’d be a^-2

when multiplying exponents with the same base, add together the exponents, so it would be -10+8

3 A circle centered at the origin has a radius
of 7 units. The terminal side of
a 210 degree angle intercepts the circle in
Quadrant III at point C. What are
the coordinates of point C?

Answers

Step-by-step explanation:

x = 7 cos 210 = 7×(-½√3) = -3.5√3

y = 7 sin 210 = 7×(-½) = -3.5

point C (-3.53 , -3.5)

One batch of walnut muffins use 1 1/3 cups of walnuts.How many cups of walnuts are needed to 3 3/4 batches of muffins, answers are only 5 cups, 3 3/12 cups, 5 1/12 cups, and 4 cups, there are no 3 1/4 cups

Answers

Answer:

5 cups

Step-by-step explanation:

Let us set it up as a fraction.

[tex]\frac{\frac{11}{3}}{1}=3\frac{\frac{3}{4}}{x}[/tex]

Step 1: Divide the given values

[tex]\frac{11}{3}\div 1 \\\\=\frac{11}{3}[/tex]

Step 2: Multiply the result by the other value

[tex]3\frac{3}{4} \\\\3\frac{3}{4} \times \frac{11}{3}\\\\= 13\frac{1}{4}[/tex]

So, with this solution, the answer is [tex]13\frac{1}{4}[/tex]. However, the answer isn't included in the options provided, so that means the answer is 5 cups.

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