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# Points J(5,2) and K(-2,-5) are two vertices

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Joined: 13 Aug 2015
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GMAT 1: 710 Q49 V38
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Points J(5,2) and K(-2,-5) are two vertices  [#permalink]

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27 Jun 2017, 15:29
6
00:00

Difficulty:

35% (medium)

Question Stats:

74% (02:37) correct 26% (02:26) wrong based on 69 sessions

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Points J(5,2) and K(-2,-5) are two vertices of an isosceles triangle. If L is the third vertex and has a y coordinate of 4, what is the x coordinate of L?

A. -5
B. -4
C. 4
D. 5
E. 6

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Joined: 16 Feb 2017
Posts: 18
Re: Points J(5,2) and K(-2,-5) are two vertices  [#permalink]

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27 Jun 2017, 18:44
mkrishnabdrr wrote:
Points J(5,2) and K(-2,-5) are two vertices of an isosceles triangle. If L is the third vertex and has a y coordinate of 4, what is the x coordinate of L?

A. -5
B. -4
C. 4
D. 5
E. 6

In an isosceles triangle only two sides are equal.
Considering JL and KL to be equal in length, we come across at below mentioned algebric equations using distance formula.

$$\sqrt{(x-5)^2+2^2}$$= $$\sqrt{(x+2)^2+9^2}$$

Squaring on both sides

$$(x-5)^2+2^2$$=$$(x+2)^2+9^2$$
$$x^2+25-10x+4=x^2+4+4x+81$$

cancelling $$x^2$$ on both ends

$$29-10x=85+4x$$
$$-14x=56$$
$$x=-4$$

Hope this helps!
Manager
Joined: 13 Aug 2015
Posts: 205
GMAT 1: 710 Q49 V38
GPA: 3.82
WE: Corporate Finance (Retail Banking)
Points J(5,2) and K(-2,-5) are two vertices  [#permalink]

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27 Jun 2017, 18:54
3
GMATAspirer09 wrote:
mkrishnabdrr wrote:
Points J(5,2) and K(-2,-5) are two vertices of an isosceles triangle. If L is the third vertex and has a y coordinate of 4, what is the x coordinate of L?

A. -5
B. -4
C. 4
D. 5
E. 6

In an isosceles triangle only two sides are equal.
Considering JL and KL to be equal in length, we come across at below mentioned algebric equations using distance formula.

$$\sqrt{(x-5)^2+2^2}$$= $$\sqrt{(x+2)^2+9^2}$$

Squaring on both sides

$$(x-5)^2+2^2$$=$$(x+2)^2+9^2$$
$$x^2+25-10x+4=x^2+4+4x+81$$

cancelling $$x^2$$ on both ends

$$29-10x=85+4x$$
$$-14x=56$$
$$x=-4$$

Hope this helps!

This problem is solvable without algebra once we identify that the points J and K are reflection on the line y=-x.
(Reflection of y=-x: (x,y)=(-y,-x)

And any point on the line y=-x will be equidistant from the points J and k.
Hence, if y coordinate =4, then x coordinate =-4

Ans is : B

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Posts: 58449
Re: Points J(5,2) and K(-2,-5) are two vertices  [#permalink]

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27 Jun 2017, 21:07
1
mkrishnabdrr wrote:
Points J(5,2) and K(-2,-5) are two vertices of an isosceles triangle. If L is the third vertex and has a y coordinate of 4, what is the x coordinate of L?

A. -5
B. -4
C. 4
D. 5
E. 6

This is a copy of the following question: https://gmatclub.com/forum/points-j-3-1 ... 89727.html
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Re: Points J(5,2) and K(-2,-5) are two vertices  [#permalink]

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19 Feb 2019, 09:08
Hello from the GMAT Club BumpBot!

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Re: Points J(5,2) and K(-2,-5) are two vertices   [#permalink] 19 Feb 2019, 09:08
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