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Intermediate Geometry : Lines

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Example Questions

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Example Question #7 : How To Find The Endpoints Of A Line Segment

The midpoint for a line with an endpoint at (3, 1) is (7, 8) . What are the coordinates for the other endpoint?

Possible Answers:

(11, 15)

(2, 6)

(15, 11)

(-1, -7)

Correct answer:

(11, 15)

Explanation:

Recall how to find the midpoint of a line:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{3+x}{2}=7$

3+x=14

x=11

Now, let's solve for the coordinate.

$\frac{y+1}{2}=8$

y+1=16

y=15

The coordinate for the other endpoint must be (11, 15) .

Report an Error

Example Question #8 : How To Find The Endpoints Of A Line Segment

A line with the endpoints (5, 1) and (a, b) has a midpoint at (-10, 2) . What are the coordinates for the unknown endpoint?

Possible Answers:

(-25, 3)

(-15, -3)

(-15, 4)

(2, -10)

Correct answer:

(-25, 3)

Explanation:

Recall how to find the midpoint of a line:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{5+a}{2}=-10$

5+a=-20

a=-25

Now, let's solve for the coordinate.

$\frac{b+1}{2}=2$

b+1=4

b=3

The coordinate for the other endpoint must be (-25, 3) .

Report an Error

Example Question #9 : How To Find The Endpoints Of A Line Segment

A line with endpoints at (-9, -2) and (c, d) has a midpoint of (5, -9) . What are the coordinates for the unknown endpoint?

Possible Answers:

(15, 12)

(19, -16)

(-14, -2)

(-20, -15)

Correct answer:

(19, -16)

Explanation:

Recall how to find the midpoint of a line:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{-9+c}{2}=5$

-9+c=10

c=19

Now, let's solve for the coordinate.

$\frac{-2+d}{2}=-9$

-2+d=-18

d=-16

The coordinate for the other endpoint must be (19, -16) .

Report an Error

Example Question #10 : How To Find The Endpoints Of A Line Segment

A line with endpoints at (-1, -2) and (e, f) has a midpoint of (8, 8) . What are the coordinates of the unknown endpoint?

Possible Answers:

(17, 18)

(16, 17)

(15, 16)

(18, 19)

Correct answer:

(17, 18)

Explanation:

Recall how to find the midpoint of a line:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{-1+e}{2}=8$

-1+e=16

e=17

Now, let's solve for the coordinate.

$\frac{-2+f}{2}=8$

-2+f=16

f=18

The coordinate for the other endpoint must be (17, 18) .

Report an Error

Example Question #31 : Midpoint Formula

A line with endpoints (6, -1) and (g, h) has a midpoint of (7, 2) . What are the coordinates of the unknown endpoint?

Possible Answers:

(8, 1)

(6, 7)

(2, 7)

(8, 5)

Correct answer:

(8, 5)

Explanation:

Recall how to find the midpoint of a line:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{6+g}{2}=7$

6+g=14

g=8

Now, let's solve for the coordinate.

$\frac{-1+h}{2}=2$

-1+h=4

h=5

The coordinate for the other endpoint must be (8,5) .

Report an Error

Example Question #32 : Midpoint Formula

A line with endpoints of (20, 2) and (j, k) has a midpoint of (7, 4) . What are the coordinates of the unknown endpoint?

Possible Answers:

(-6 ,8)

(-8, 8)

(-6, 6)

(6, -6)

Correct answer:

(-6, 6)

Explanation:

Recall how to find the midpoint of a line:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{20+j}{2}=7$

20+j=14

j=-6

Now, let's solve for the coordinate.

$\frac{k+2}{2}=4$

k+2=8

k=6

The coordinate for the other endpoint must be (-6, 6) .

Report an Error

Example Question #33 : Midpoint Formula

A line with endpoints (5, 5) and (l, m) has a midpoint of (-1, 1) . What are the coordinates of the unknown endpoint?

Possible Answers:

(6, 1)

(1, 10)

(-7, -3)

(-5, -2)

Correct answer:

(-7, -3)

Explanation:

Recall how to find the midpoint of a line:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{5+l}{2}=-1$

5+l=-2

l=-7

Now, let's solve for the coordinate.

$\frac{m+5}{2}=1$

m+5=2

m=-3

The coordinate for the other endpoint must be (-7, -3) .

Report an Error

Example Question #34 : Midpoint Formula

A line with endpoints of (12, -10) and (x, y) has a midpoint of (6, 2) . What are the coordinates of the unknown endpoint?

Possible Answers:

(12, 2)

(0, 14)

(8, 0)

(15, 1)

Correct answer:

(0, 14)

Explanation:

Recall how to find the midpoint of a line:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{12+x}{2}=6$

12+x=12

x=0

Now, let's solve for the coordinate.

$\frac{-10+y}{2}=2$

-10+y=4

y=14

The coordinate for the other endpoint must be (0, 14) .

Report an Error

Example Question #35 : Midpoint Formula

A line with endpoints of (-3, 5) and (x, y) has a midpoint of (6, 1) . What are the coordinates of the unknown endpoint?

Possible Answers:

(15, -3)

(16, 2)

(14, -2)

(3, 18)

Correct answer:

(15, -3)

Explanation:

Recall how to find the midpoint of a line:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{-3+x}{2}=6$

-3+x=12

x=15

Now, let's solve for the coordinate.

$\frac{5+y}{2}=1$

5+y=2

y=-3

The coordinate for the other endpoint must be (15, -3) .

Report an Error

Example Question #36 : Midpoint Formula

A line with endpoints of (4, -4) and (x, y) has a midpoint of (8, 8) . What are the coordinates of the unknown endpoint?

Possible Answers:

(12, 20)

(13, 20)

(15, 20)

(16, 20)

Correct answer:

(12, 20)

Explanation:

Recall how to find the midpoint of a line:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{4+x}{2}=8$

4+x=16

x=12

Now, let's solve for the coordinate.

$\frac{-4+y}{2}=8$

-4+y=16

y=20

The coordinate for the other endpoint must be (12, 20) .

Report an Error

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Intermediate Geometry : Lines

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #7 : How To Find The Endpoints Of A Line Segment

Example Question #8 : How To Find The Endpoints Of A Line Segment

Example Question #9 : How To Find The Endpoints Of A Line Segment

Example Question #10 : How To Find The Endpoints Of A Line Segment

Example Question #31 : Midpoint Formula

Example Question #32 : Midpoint Formula

Example Question #33 : Midpoint Formula

Example Question #34 : Midpoint Formula

Example Question #35 : Midpoint Formula

Example Question #36 : Midpoint Formula

All Intermediate Geometry Resources

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