Source: Manhattan Prep
Three of the four vertices of a rectangle in the xy-coordinate plane are (-5,1), (-4,4), and (8,0). What is the fourth vertex?
A. (-4.5, 2.5)
B. (-4, 5)
C. (6, -2)
D. (7, -3)
E. (10, 1)
The OA is D.
Three of the four vertices of a rectangle in the xy
This topic has expert replies
-
- Moderator
- Posts: 2205
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
-
- Junior | Next Rank: 30 Posts
- Posts: 25
- Joined: Mon May 07, 2018 8:47 am
- Location: India
- GMAT Score:610
Please refer to the attached figure.
Since the figure is rectangle. The lines BD and DE are perpendicular to each other (Point E is the unknown vertex)
Product of slopes of 2 lines perpendicular to each other is -1
from the figure we have slope of BD = (0 - 4)/(8-(-4)) = -4/12 = -1/3
Hence, Slope of line DE will be = (-1)/(-1/3) = 3
From the figure, we can see that x-coordinate of unknown vertex is positive while y-coordinate is negative. Hence, A, B and E are out
Plugging in C and D to check with which vertex we can obtain slope of 3:
C : (-2-0)/(6-8) = -2/-2 = 1
D: (-3-0)(7-8) = 3
Hence, D is the correct answer
Since the figure is rectangle. The lines BD and DE are perpendicular to each other (Point E is the unknown vertex)
Product of slopes of 2 lines perpendicular to each other is -1
from the figure we have slope of BD = (0 - 4)/(8-(-4)) = -4/12 = -1/3
Hence, Slope of line DE will be = (-1)/(-1/3) = 3
From the figure, we can see that x-coordinate of unknown vertex is positive while y-coordinate is negative. Hence, A, B and E are out
Plugging in C and D to check with which vertex we can obtain slope of 3:
C : (-2-0)/(6-8) = -2/-2 = 1
D: (-3-0)(7-8) = 3
Hence, D is the correct answer