What's the midpoint of a line segment joining the points (5, –4) and (–13, 12)?
Question 8 options:

A)

(–4, 4)

B)

(9, 4)

C)

(–4, 8)

D)

(4, 4)

Answers

Answer 1

Answer:

The midpoint of the line segment is located at (-4, 4).

Step-by-step explanation:

We're given the coordinate points of a line that can help us find the midpoint.

The midpoint formula for a line is written as:

[tex]\bullet \ \ \ \displaystyle\big(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\big)[/tex]

Additionally, we are given the coordinate points (5, -4) and (-13, 12). We can use these and label them with the (x, y) system so we can substitute them into the formula.

In math, a coordinate pair is written as (x, y). This is where cos = x and sin = y. If we are given two coordinate pairs, we can label them with the (x, y) system but also incorporating a subscript to distinguish the two x-values from each other as well as the y-values. We do this by turning the two x-values into x₁ and x₂ and the y-values follow the same protocol: y₁ and y₂.

Therefore, we can label our two coordinates:

(5, -4)

x₁ = 5y₁ = -4

(-13, 12)

x₂ = -13y₂ = 12

Now, we can place these values into the midpoint formula and simplify to find our midpoint.

Recall that the midpoint formula is:

[tex]\bullet \ \ \ \displaystyle\big(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\big)[/tex]

Therefore, let's substitute these values.

[tex]\displaystyle\big(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\big)\\\\\\\big(\frac{5 + (-13)}{2}, \frac{(-4)+12}{2}\big)\\\\\\\big(\frac{-8}{2}, \frac{8}{2}\big)\\\\\\\boxed{(-4, 4)}[/tex]

Therefore, the midpoint of the line segment is located at (-4, 4), which is Option A.

Answer 2

Answer: Great question! A midpoint is exactly what it sounds like; the point in the middle of two objects (in this case it's the middle of these two coordinates). Another way to think of the middle of something in math is by using the average. To find the midpoint of two points, we just find the average of the x-values and the average of the y-values:

(x1 + x2)/2 , (y1 + y2)/2)

(5 + -13) / 2 , (-4 + 12) / 2)

( -8 / 2 , 8 / 2)

(-4 , 4)

So the answer would be A)

(-4, 4)

Explanation:

let ( x,y) be the midpoint of the line segment, then x =  5+(-13) / 2 = -8/2 = -4 and y = -4+(12 ) / 2 = 8/2 = 4, the mid point is ( -4,4)


Related Questions

There are three times as many girls as boys in a school .Find an expression in term of x for the total number of student in school ,where x represent the number of boys in the school

Answers

Answer:

Total number of students = 4x

Step-by-step explanation:

Let the number of boys be x

Since, no of girls = 3 times the no of boys

So, number of girls = 3x

Total number of students = no of boys + no of girls

Total number of students = x + 3x

Total number of students = 4x

Answer:

The total number of students is 4x

Step-by-step explanation:

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Answer:

The third side is 36 units.

Step-by-step explanation:

Given that this is a 90° triangle so you can apply Pythagoras Theorem :

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {a}^{2} = {c}^{2} - {b}^{2} [/tex]

[tex] {a}^{2} = {( \sqrt{90}) }^{2} - {6}^{2} [/tex]

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A scuba diver is 20 feet below the surface of the water 14 seconds after he entered the water and 100 feet below the surface after 30 seconds.  What is the scuba divers rate of change?

Answers

Answer:

1 foot = 0.7 secs

Step-by-step explanation:

14 seconds divided by 20 feet = 0.7 seconds per foot descended.

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Look at points C and D on the graph. What is the distance (in units) between points C and D? Round your answer to the nearest hundredth. I REALLY NEED IT FAST

Answers

Answer:

The distance between points C and D is 5.83

Step-by-step explanation:

We need to find distance between points C and D

Looking at the graph we can find coordinates (x,y) of points C and D

Coordinates of point C are: (-4,3)

Coordinates of point D are: (1,0)

The formula used to calculate Distance is:

[tex]Distance=\sqrt{(x_2-x_1)^+(y_2-y_1)^2}[/tex]

Putting values and finding distance between points C and D

[tex]x_1=-4, y_1=3, x_2=1, y_2=0[/tex]

[tex]Distance=\sqrt{(x_2-x_1)^+(y_2-y_1)^2}\\Distance=\sqrt{(1-(-4))^2+(0-3)^2} \\Distance=\sqrt{(1+4)^2+(-3)^2} \\Distance=\sqrt{(5)^2+(-3)^2} \\Distance=\sqrt{25+9}\\Distance=\sqrt{34}\\ Distance=5.83[/tex]

So, the distance between points C and D is 5.83

Plz help The population of a specific species of a nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted

How many mammals were there when they were originally counted?

Enter your answer in the box​

Answers

Answer:

The y-intercept represents the number of mammals when they were originally counted.

The y-intercept.is 75.

The asymptote indicates that the number of mammals counted when the study began was 120.

The asymptote indicates that as years pass, the number of mammals will approach 0.

Step-by-step explanation:

im a lil late but here ya go and for anyone further who needs these answers.. Its kind of obvious thugh just by looking at the graph what the answers are.

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Answers

Answer:

34, 15, -4, -23 and -42

Step-by-step explanation:

We are to find the first five sequence

when n = 1

f(2) = f(1) - 19

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f(2) = 15

when n = 2

f(2+1) = f(2) - 19

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Answers

Answer:

Third choice

Step-by-step explanation:

We can subtract 4r by r, and that gives 3r. 3 subtracted by negative 3 gives 6 (Remember, 2 negatives is a positive!). This gives 3r+6

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What is the polar form of (x + 3)2 + y2 = 9?

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r = −3 cos(θ)
r = 3 cos(θ)
r = 6 cos(θ)

Answers

Answer:

r = -6 cos(θ)

Step-by-step explanation:

got it right on edge

The equation (x + 3)² + y² = 9 into polar form is r = -6 cos(θ). The correct answer would be option (A).

What is the polar form?

The polar form of a complex number is given by r(cos(θ) + i sin(θ)), where r is the distance from the origin and θ is the angle formed by the point and the positive x-axis.

To convert the equation (x + 3)² + y² = 9 into polar form, we can complete the square on the x and y terms:

(x + 3)² + y² = (x² + 6x + 9) + y² = 9

Then we can express x and y in terms of r and θ:

x = r cos(θ) , y = r sin(θ)

Substituting these values into the equation and simplifying:

r² cos²(θ) + 6r cos(θ) + r² sin²(θ) = 9

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r = -6cos(θ)

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What is the simplified form of 15 x to the eighth power over 24 y to the fifth power divided by 4 x to the fourth power over 8 squared ? (6 points)

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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b

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Answer:

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Answer:

(5v−8)(5v2+7)

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Answers Are

Answers

Answer:

C. Because they have the same slopes and different y-intercepts

Step-by-step explanation:

Answer:

Your answer would be the 3rd one.

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1. A sweater for $19.99 and a 6% sales tax. _______________________________________
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4. A TV for $3000.00 and a 4% sales tax.___________________________________________
5. A radio for $35.00 and a 6% sales tax.____________________________________________

Answers

Answer:

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1. The sales tax of a sweater = $1.2

2. The sales tax of a purse = $2.25

3. The sales tax of a bicycle =  $8.4

4. The sales tax of a TV = $120

5. The sales tax of a radio = $2.1

What is a percentage?

A ratio or value that may be stated as a fraction of 100 is called a percentage. Moreover, it is indicated by the symbol "%."

Given:

1. A sweater for $19.99 and a 6% sales tax.

The sales tax of a sweater = 19.99 x 0.06 = $1.2

2. A purse for $45.00 and a 5% sales tax.

The sales tax of a purse = 45 x 0.05 = $2.25

3. A bicycle for $120.00 and a 7% sales tax.

The sales tax of a bicycle = 120 x 0.07 = $8.4

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Mikah and Gracie were running laps at the local gym. Mikah ran 1 and 4/8 laps, and Gracie ran 1 and 1/2 laps. Who ran a further distance?

Answers

Answer:

Trick question they both ran equal distance

Step-by-step explanation:

Gracies distand 1 and 1/2 is already in simplist form, but Mikahs distance 1 and 4/8 can be reduced.

More specifically the fration 4/8 can be reduced, finding the largest common multiple between 4 and 8 we find that 4 is the largest number that goes into both.

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Isosceles Right

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Step-by-step explanation:

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Used:

[tex]\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\\sqrt{a}=b\iff b^2=a\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\\sqrt{16}=4\ \text{because}\ 4^2=16[/tex]

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