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23 Jun 2022, 01:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
24% (03:26) correct
76%
(02:16)
wrong
based on 34
sessions
History
Date
Time
Result
Not Attempted Yet
A triangle with vertices (6, 5), (8, -3), and (9, 1) is reflected about the line x = 8 to create a second triangle. What is the area of the union of the two triangles?
(A) 9
(B) 28/3
(C) 10
(D) 31/3
(E) 32/3
Are You Up For the Challenge: 700 Level Questions
(A) 9
(B) 28/3
(C) 10
(D) 31/3
(E) 32/3
Are You Up For the Challenge: 700 Level Questions
23 Jun 2022, 22:35
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Bunuel
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PS Gmat club question.png [ 65.53 KiB | Viewed 4168 times ]
we need to determine the y coordinate of point F.
Equate the slopes of the lines BF & FC
\(\frac{5-y}{6-8} = \frac{y-1}{8-9}\)
\(\frac{5-y}{-2} = \frac{y-1}{-1}\)
\(5-y = 2y-2\)
\(3y = 7\)
\(y = \frac{7}{3}\)
Area of figure ABFE = \(2 *\triangle ABF\) = \(2 * \frac{1}{2} * (8-6) * (\frac{7}{3} + 3) = 2 * \frac{16}{3} = \frac{32}{3}\)
Hence, the answer is E.
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