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

[Mike@Magoosh]

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/

Mike

[GMATinsight]

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

[Mathsbuddy]

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.

[ahmedshafea]

Is the above reply a correct solution? If not could one explain the steps please

[Matt@VeritasPrep]

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.)