|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
24 Mar 2022, 01:31
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
83% (02:32) correct
17%
(03:18)
wrong
based on 133
sessions
History
Date
Time
Result
Not Attempted Yet
In a coordinate grid, if the points D(–1, –1), E(–1, 1), F(a, 1), and G(a, –1) are the vertices of a rectangle with a diagonal length of \(2\sqrt{5}\), then what is the value of a?
A. 3
B. 5
C. \(3 \sqrt{5}\)
D. 9
E. \(7 \sqrt{3}\)
A. 3
B. 5
C. \(3 \sqrt{5}\)
D. 9
E. \(7 \sqrt{3}\)
24 Mar 2022, 06:43
Kudos
Bookmarks
The width of the rectangle is the distance between (-1, -1) and (-1, 1), which is 2. We don't know the length L of the rectangle, but we know the diagonal is 2√5, so using Pythagoras we find
\(\\
\begin{align}\\
2^2 + L^2 &= (2 \sqrt{5} )^2 \\\\
4 + L^2 &= 2^2 (\sqrt{5})^2 \\\\
L^2 &= 20 - 4 \\\\
L^2 &= 16 \\\\
L &= 4\\
\end{align}\\
\)
since L is positive. So the two other points of the rectangle are 4 units horizontally across from the two points D and E that we're given, and the x coordinate of those two points could either be -1 - 4 = -5 if the two unknown points are to the left of D and E, or could be -1 + 4 = 3 if the two unknown points are to the right of D and E. So I imagine the "OA" is "3", but the question has two right answers, while the wording of the question suggests it only has one, so there's a problem with the question.
\(\\
\begin{align}\\
2^2 + L^2 &= (2 \sqrt{5} )^2 \\\\
4 + L^2 &= 2^2 (\sqrt{5})^2 \\\\
L^2 &= 20 - 4 \\\\
L^2 &= 16 \\\\
L &= 4\\
\end{align}\\
\)
since L is positive. So the two other points of the rectangle are 4 units horizontally across from the two points D and E that we're given, and the x coordinate of those two points could either be -1 - 4 = -5 if the two unknown points are to the left of D and E, or could be -1 + 4 = 3 if the two unknown points are to the right of D and E. So I imagine the "OA" is "3", but the question has two right answers, while the wording of the question suggests it only has one, so there's a problem with the question.
24 Mar 2022, 19:07
Kudos
Bookmarks
One side of rectangle = 1-(-1) =2
So, 2^2 + b^2 = {2 sqrt(5)}^2 and, b= another side of rectangle = 4.
And, a-(-1) = 4 or, a = 3. So, I think A.
So, 2^2 + b^2 = {2 sqrt(5)}^2 and, b= another side of rectangle = 4.
And, a-(-1) = 4 or, a = 3. So, I think A.
