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Points J (3, 1) and K (– 1, – 3) are two vertices of an

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by Mike@Magoosh » Mon Dec 08, 2014 2:59 pm
Points J (3, 1) and K (– 1, – 3) are two vertices of an isosceles triangle. If L is the third vertex and has a y-coordinate of 6, what is the x-coordinate of L?
(A) –3
(B) –4
(C) –5
(D) –6
(E) –7

For a collection of Coordinate Geometry practice problems, as well as for the OA & OE of this particular problem, see:
https://magoosh.com/gmat/2014/gmat-prac ... -geometry/

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by GMATinsight » Wed Dec 10, 2014 3:07 am
Mike@Magoosh wrote:Points J (3, 1) and K (– 1, – 3) are two vertices of an isosceles triangle. If L is the third vertex and has a y-coordinate of 6, what is the x-coordinate of L?
(A) –3
(B) –4
(C) –5
(D) –6
(E) –7
Answer: Option D
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by Mathsbuddy » Wed Dec 10, 2014 7:27 am
Upon visualising the given coordinates it is easy (and fast) to realise that the triangle is symmetrical about the line y = -x. Therefore, if the x co-ordinate of the third vertx is 6, then the y co-ordinate must be -6.
No need for any trig or Pythagoras.
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by ahmedshafea » Wed Aug 30, 2017 12:30 pm
Is the above reply a correct solution? If not could one explain the steps please
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by Matt@VeritasPrep » Wed Aug 30, 2017 6:00 pm
ahmedshafea wrote:Is the above reply a correct solution? If not could one explain the steps please
Pretty much. (3, 1) and (-1, -3) are equidistant from (2, -2), and from there the solution follows. (You could also treat (2, -2) as the midpoint of the base, then work with isosceles properties.)
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