Intermediate Geometry : How to find the endpoints of a line segment

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #21 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at \displaystyle (11, -2) and a midpoint at \displaystyle (5, 0). Find the coordinates of the other endpoint.

Possible Answers:

\displaystyle (3, -2)

\displaystyle (2, 1)

\displaystyle (-1, 0)

\displaystyle (-1, 2)

Correct answer:

\displaystyle (-1, 2)

Explanation:

Recall how to find the midpoint of a line segment:

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

where \displaystyle (x_1, y_1)\text{ and}(y_1, y_2) are the endpoints.

Let's first focus on the \displaystyle x coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{11+x_2}{2}=5

Solve for \displaystyle x_2.

\displaystyle 11+x_2=10

\displaystyle x_2=-1

Next, find the \displaystyle y coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{-2+y_2}{2}=0

\displaystyle -2+y_2=0

\displaystyle y_2=2

The second endpoint must be at \displaystyle (-1, 2).

 

Example Question #41 : Midpoint Formula

A line segment has an endpoint at \displaystyle (-24, 12) and midpoint at \displaystyle (30, -5). Find the coordinates of the other endpoint.

Possible Answers:

\displaystyle (80, -40)

\displaystyle (92, -15)

\displaystyle (84, -22)

\displaystyle (90, -24)

Correct answer:

\displaystyle (84, -22)

Explanation:

Recall how to find the midpoint of a line segment:

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

where \displaystyle (x_1, y_1)\text{ and}(y_1, y_2) are the endpoints.

Let's first focus on the \displaystyle x coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{-24+x_2}{2}=30

Solve for \displaystyle x_2.

\displaystyle -24+x_2=60

\displaystyle x_2=84

Next, find the \displaystyle y coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{12+y_2}{2}=-5

\displaystyle 12+y_2=-10

\displaystyle y_2=-22

The second endpoint must be at \displaystyle (84, -22).

 

Example Question #23 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at \displaystyle (1, 7) and midpoint at \displaystyle (5, 0). Find the coordinates of the other endpoint.

Possible Answers:

\displaystyle (9, -7)

\displaystyle (8, -6)

\displaystyle (12, -9)

\displaystyle (10, -2)

Correct answer:

\displaystyle (9, -7)

Explanation:

Recall how to find the midpoint of a line segment:

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

where \displaystyle (x_1, y_1)\text{ and}(y_1, y_2) are the endpoints.

Let's first focus on the \displaystyle x coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{1+x_2}{2}=5

Solve for \displaystyle x_2.

\displaystyle 1+x_2=10

\displaystyle x_2=9

Next, find the \displaystyle y coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{7+y_2}{2}=0

\displaystyle 7+y_2=0

\displaystyle y_2=-7

The second endpoint must be at \displaystyle (9 -7).

 

Example Question #42 : Lines

A line segment has an endpoint at \displaystyle (-2, 5) and midpoint at \displaystyle (11, 2). Find the coordinates of the other endpoint.

Possible Answers:

\displaystyle (26, -10)

\displaystyle (22, -2)

\displaystyle (24, -1)

\displaystyle (19, 1)

Correct answer:

\displaystyle (24, -1)

Explanation:

Recall how to find the midpoint of a line segment:

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

where \displaystyle (x_1, y_1)\text{ and}(y_1, y_2) are the endpoints.

Let's first focus on the \displaystyle x coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{-2+x_2}{2}=11

Solve for \displaystyle x_2.

\displaystyle -2+x_2=22

\displaystyle x_2=24

Next, find the \displaystyle y coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{5+y_2}{2}=2

\displaystyle 5+y_2=4

\displaystyle y_2=-1

The second endpoint must be at \displaystyle (24, -1).

 

Example Question #41 : Lines

A line segment has an endpoint at \displaystyle (-2, -4) and midpoint at \displaystyle (-5, 0). Find the coordinates of the other endpoint.

Possible Answers:

\displaystyle (2, 4)

\displaystyle (-8, 4)

\displaystyle (-12, 12)

\displaystyle (-10, 8)

Correct answer:

\displaystyle (-8, 4)

Explanation:

Recall how to find the midpoint of a line segment:

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

where \displaystyle (x_1, y_1)\text{ and}(y_1, y_2) are the endpoints.

Let's first focus on the \displaystyle x coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{-2+x_2}{2}=-5

Solve for \displaystyle x_2.

\displaystyle -2+x_2=-10

\displaystyle x_2=-8

Next, find the \displaystyle y coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{-4+y_2}{2}=0

\displaystyle -4+y_2=0

\displaystyle y_2=4

The second endpoint must be at \displaystyle (-8, 4).

 

Example Question #41 : Lines

A line segment has an endpoint at \displaystyle (3, 16) and midpoint at \displaystyle (14, 7). Find the coordinates of the other endpoint.

Possible Answers:

\displaystyle (15, -2)

\displaystyle (27, -3)

\displaystyle (2, -12)

\displaystyle (25, -2)

Correct answer:

\displaystyle (25, -2)

Explanation:

Recall how to find the midpoint of a line segment:

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

where \displaystyle (x_1, y_1)\text{ and}(y_1, y_2) are the endpoints.

Let's first focus on the \displaystyle x coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{3+x_2}{2}=14

Solve for \displaystyle x_2.

\displaystyle 3+x_2=28

\displaystyle x_2=25

Next, find the \displaystyle y coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{16+y_2}{2}=7

\displaystyle 16+y_2=14

\displaystyle y_2=-2

The second endpoint must be at \displaystyle (25, -2).

 

Example Question #1331 : Intermediate Geometry

A line segment has an endpoint at \displaystyle (8, -2) and midpoint at \displaystyle (1, -1). Find the coordinates of the other endpoint.

Possible Answers:

\displaystyle (2, 10)

\displaystyle (-6, 0)

\displaystyle (-5, 0)

\displaystyle (2, 0)

Correct answer:

\displaystyle (-6, 0)

Explanation:

Recall how to find the midpoint of a line segment:

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

where \displaystyle (x_1, y_1)\text{ and}(y_1, y_2) are the endpoints.

Let's first focus on the \displaystyle x coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{8+x_2}{2}=1

Solve for \displaystyle x_2.

\displaystyle 8+x_2=2

\displaystyle x_2=-6

Next, find the \displaystyle y coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{-2+y_2}{2}=-1

\displaystyle -2+y_2=-2

\displaystyle y_2=0

The second endpoint must be at \displaystyle (-6, 0).

 

Example Question #22 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at \displaystyle (9, -3) and midpoint at \displaystyle (12, -8). Find the coordinates of the other endpoint.

Possible Answers:

\displaystyle (15, -13)

\displaystyle (19, -4)

\displaystyle (16, -21)

\displaystyle (17, -18)

Correct answer:

\displaystyle (15, -13)

Explanation:

Recall how to find the midpoint of a line segment:

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

where \displaystyle (x_1, y_1)\text{ and}(y_1, y_2) are the endpoints.

Let's first focus on the \displaystyle x coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{9+x_2}{2}=12

Solve for \displaystyle x_2.

\displaystyle 9+x_2=24

\displaystyle x_2=15

Next, find the \displaystyle y coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{-3+y_2}{2}=-8

\displaystyle -3+y_2=-16

\displaystyle y_2=-13

The second endpoint must be at \displaystyle (15, -13).

 

Example Question #23 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at \displaystyle (17, 2) and midpoint at \displaystyle (6, 8). Find the coordinates of the other endpoint.

Possible Answers:

\displaystyle (18, 17)

\displaystyle (18, 20)

\displaystyle (16, 12)

\displaystyle (15, 14)

Correct answer:

\displaystyle (15, 14)

Explanation:

Recall how to find the midpoint of a line segment:

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

where \displaystyle (x_1, y_1)\text{ and}(y_1, y_2) are the endpoints.

Let's first focus on the \displaystyle x coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{17+x_2}{2}=6

Solve for \displaystyle x_2.

\displaystyle 17+x_2=32

\displaystyle x_2=15

Next, find the \displaystyle y coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{2+y_2}{2}=8

\displaystyle 2+y_2=16

\displaystyle y_2=14

The second endpoint must be at \displaystyle (15, 14).

 

Example Question #24 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at \displaystyle (-2, 4) and a midpoint at \displaystyle (12, 2). Find the other endpoint.

Possible Answers:

\displaystyle (30, 4)

\displaystyle (28, -2)

\displaystyle (-14, 22)

\displaystyle (26, 0)

Correct answer:

\displaystyle (26, 0)

Explanation:

Recall how to find the midpoint of a line segment:

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

where \displaystyle (x_1, y_1)\text{ and}(y_1, y_2) are the endpoints.

Let's first focus on the \displaystyle x coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{-2+x_2}{2}=12

Solve for \displaystyle x_2.

\displaystyle -2+x_2=24

\displaystyle x_2=26

Next, find the \displaystyle y coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

\displaystyle \frac{4+y_2}{2}=2

\displaystyle 4+y_2=4

\displaystyle y_2=0

The second endpoint must be at \displaystyle (26, 0)

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