GRE Math : How to find the endpoints of a line segment

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Example Question #1 : How To Find The Endpoints Of A Line Segment

There is a line defined by two end-points, (4,3) and (a,b) . The midpoint between these two points is (7,15) . What is the value of the point (a,b) ?

Possible Answers:

(14,-1)

(3,12)

(12,3)

(13,41)

(10,27)

Correct answer:

(10,27)

Explanation:

Recall that to find the midpoint of two points (a,b) and (c,d) , you use the equation:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$ .

(It is just like finding the average of the two points, really.)

So, for our equation, we know the following:

$\left(\frac{4+a}{2},\frac{3+b}{2}\right)=(7,15)$

You merely need to solve each coordinate for its respective value.

$\frac{4+a}{2}=7$

4+a=14

a=10

Then, for the y-coordinate:

$\frac{3+b}{2}=15$

3+b=30

b=27

Therefore, our other point is: (10,27)

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Example Question #2 : How To Find The Endpoints Of A Line Segment

There is a line defined by two end-points, (11,-5) and (a,b) . The midpoint between these two points is (-6,-21) . What is the value of the point (a,b) ?

Possible Answers:

(12,-14)

(-23,-37)

(5,-26)

(4,-194)

(-14,-25)

Correct answer:

(-23,-37)

Explanation:

Recall that to find the midpoint of two points (a,b) and (c,d) , you use the equation:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$ .

(It is just like finding the average of the two points, really.)

So, for our equation, we know the following:

$\left(\frac{11+a}{2},\frac{-5+b}{2}\right)=(-6,-21)$

You merely need to solve each coordinate for its respective value.

$\frac{11+a}{2}=-6$

11+a=-12

a=-23

Then, for the y-coordinate:

$\frac{-5+b}{2}=-21$

-5+b=-42

b=-37

Therefore, our other point is: (-23,-37)

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Example Question #3 : How To Find The Endpoints Of A Line Segment

What is the other endpoint of a line segment with one point that is (6,8) and a midpoint of (14,1) ?

Possible Answers:

(22,8)

(12,7)

(-15,-6)

(7,16)

(22,-6)

Correct answer:

(22,-6)

Explanation:

Recall that the midpoint formula is like finding the average of the and values for two points. For two points (a,b) and (c,d) , it is:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$

For our points, we are looking for (c,d) . We know:

$\left(\frac{6+c}{2},\frac{8+d}{2}\right)=(14,1)$

We can solve for each of these coordinates separately:

X-Coordinate

$\frac{6+c}{2} = 14$

6+c=28

c=22

Y-Coordinate:

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

8+d=2

d=-6

Therefore, our point is (22,-6)

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Example Question #1 : How To Find The Endpoints Of A Line Segment

What is the other endpoint of a line segment with one point that is (-15,14) and a midpoint of (-19,4) ?

Possible Answers:

(-12,-9)

(-23,-6)

(-14,-14)

(-20,-12)

(14,17)

Correct answer:

(-23,-6)

Explanation:

What is the other endpoint of a line segment with one point that is (-15,14) and a midpoint of (-19,4) ?

Recall that the midpoint formula is like finding the average of the and values for two points. For two points (a,b) and (c,d) , it is:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$

For our points, we are looking for (c,d) . We know:

$\left(\frac{-15+c}{2},\frac{14+d}{2}\right)=(-19,4)$

We can solve for each of these coordinates separately:

X-Coordinate

$\frac{-15+c}{2}=-19$

-15+c=-38

c=-23

Y-Coordinate:

$\frac{14+d}{2}=4$

14+d=8

d=-6

Therefore, our point is (-23,-6)

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GRE Math : How to find the endpoints of a line segment

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Example Question #1 : How To Find The Endpoints Of A Line Segment

Example Question #2 : How To Find The Endpoints Of A Line Segment

Example Question #3 : How To Find The Endpoints Of A Line Segment

Example Question #1 : How To Find The Endpoints Of A Line Segment

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