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15 Dec 2017, 02:05
Kudos
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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:
25%
(medium)
Question Stats:
78% (02:02) correct
23%
(02:30)
wrong
based on 120
sessions
History
Date
Time
Result
Not Attempted Yet
In ∆ ABC shown above, AB = BC and base AC is equal to the altitude of the triangle from point B. If the coordinates of points A and C are (2, 5) and (6, 5) respectively, which of the following could be the coordinates of point B?
(A) (2, 7)
(B) (2, 8)
(C) (2, 9)
(D) (4, 8)
(E) (4, 9)
Attachment:
2017-12-15_1258_001.png [ 4.47 KiB | Viewed 5061 times ]
15 Dec 2017, 08:23
Kudos
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Hi
The answer is E.
My explanation is as per attached sketch.
Please see how we can easily eliminate the choices A, B & C in a few seconds.
if you like the approach, appreciate by kudos.
The answer is E.
My explanation is as per attached sketch.
Please see how we can easily eliminate the choices A, B & C in a few seconds.
if you like the approach, appreciate by kudos.
Bunuel
Attachments
WhatsApp Image 2017-12-15 at 20.54.16.jpeg [ 102.63 KiB | Viewed 4614 times ]
15 Dec 2017, 10:03
Kudos
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Bunuel
Four answers can be rejected quickly: A, B, C, and D.
The prompt makes it easy to find B's y-coordinate. We are given that the altitude from point B = base AC. Add the length of AC to 5 to find B's y-coordinate.
Length of AC: (6 - 2) = 4
Points A and C (and AC) are at y=5. Add the 4
(5 + 4) = 9 = B's y-coordinate
Eliminate answers A, B, and D, whose y-coordinates are not 9
Also eliminate Answer C (2, 9), for a number of reasons.* If B is at (2,9), directly above A, we now have a right isosceles triangle where AB = AC and hypotenuse BC does NOT equal AB. BC must = AC. Reject C.
Answer E is correct
AB = BC: ∆ ABC is isosceles. Its altitude is a perpendicular bisector of the base AC.
The altitude from B hits the base at AC's midpoint (4,5). The x-coordinate for AC's midpoint is (2+6)/2 = 4. The x-coordinate of B must be 4.
B is at (4,9)
Answer E
*If that doesn't stand out, think of side lengths and angle measures. AB = BC, so
∠A = ∠C (angles opposite equal sides are equal).
Imagine B "moving" to directly above A: ∠A gets bigger, ∠C gets smaller. Not possible; they're equal. Side AB gets shorter, side BC gets longer. Also not possible: AB = BC
