In the coordinate geometry plane, point A is the midpoint

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sat Jan 05, 2019 6:42 am

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In the coordinate geometry plane, point A is the midpoint between points (5,8) and (-3, -2). If the midpoint between point A and point B is (4, -1), in which quadrant does point B lie?

A. I
B. II
C. III
D. IV
E. None of the above

[spoiler]OA=D[/spoiler]

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Sat Jan 05, 2019 6:42 am

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by [email protected] » Sun Jan 06, 2019 11:39 am

Hi VJesus12,

This question can be solved with a bit of general graphing (you do not need to be hyper-accurate with your drawing to get the correct answer).

To start, we're told that in the coordinate geometry plane, Point A is the midpoint between points (5,8) and (-3, -2). Draw those two points on a graph and draw a line connecting them. Since (5,8) is so much 'further in' to Quadrant 1 than (-3,-2) is into Quadrant 3, the midpoint (Point A) will clearly be in Quadrant 1.

Next, graph the point (4, -1). Draw a line from Point A to this new point. This point is "down and to the right" from Point A.... and since this new point is the midpoint between Point A and Point B, we know that extending that line further "down and to the right" would lead us to Point B. Thus, Point B would clearly be in Quadrant 4.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8134; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Jan 27, 2019 6:29 pm

VJesus12 wrote:In the coordinate geometry plane, point A is the midpoint between points (5,8) and (-3, -2). If the midpoint between point A and point B is (4, -1), in which quadrant does point B lie?

A. I
B. II
C. III
D. IV
E. None of the above

Using the midpoint formula, [(x_1 + x_2)/2 , (y_1 + y_2)/2], we can calculate the coordinates of point A:

[(5 - 3)/2, (8 - 2)/2] = (1, 3)

Now, let the coordinates of point B be (x, y). Using the midpoint formula again, we can create the equation:

((1 + x)/2, (3 + y)/2) = (4, -1)

This means (1 + x)/2 = 4 and (3 + y)/2 = -1. So we have:

(1 + x)/2 = 4 â†’ 1 + x = 8 â†’ x = 7 and (3 + y)/2 = -1 â†’ 3 + y = -2 â†’ y = -5

So the coordinates of point B is (7, -5), which is in quadrant IV.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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