Problem Solving

The base of an isosceles triangle has the coordinates (5,2) and (1,2). Which coordinate could be the third vertex of the triangle?

Check all that apply

(4,7)
(4,-7)
(3,6)
(5,-6)
(3,-6)


This is a GRE question btw but I'm sure the concept tested is the same on GMAT.

[spoiler](3,6) & (3,-6)[/spoiler]

Please explain

base of the triangle is (5,2) & (1,2)...if you look carefully you will notice that base is parallel to x axis (y = 2 for both points). Now we know that in isosceles triangle the sides other than base are of equal length and meet at the point which lies on the perpendicular bisector of the base...

so mid point of base is (3,2) => since the third point is perpendicular to midpoint ...third point will have x coordinate = 3

and this is given in choices [spoiler](3,6) and (3,-6)[/spoiler]

I hope this explains...

Anurag@Gurome wrote:

MBA.Aspirant wrote:Please explain

Solution:
Now, any point on the perpendicular bisector of the line segment joining (5,2) and (1, 2) will be equidistant from the above two points.
So,that point when joined to (5, 2) and (1, 2) will make an isosceles triangle.
Also,the perpendicular bisector will pass through the mid point of the line segment which is (3, 2) and its equation will be x = 3.
Hence, any point with x-coordinate 3 will make an isosceles triangle.
Both (3, 6) and (3, -6) satisfy this condition.

Thanks Dr. Anurag

SUHAILK wrote:Now we know that in isosceles triangle the sides other than base are of equal length and meet at the point which lies on the perpendicular bisector of the base...

Thanks for ur help. I didn't know that

just check for the distances here.

(18)^1/2 fits in for (3,6) and (-3,6).

Anurag@Gurome wrote:

MBA.Aspirant wrote:Please explain

Solution:
Now, any point on the perpendicular bisector of the line segment joining (5,2) and (1, 2) will be equidistant from the above two points.
So,that point when joined to (5, 2) and (1, 2) will make an isosceles triangle.
Also,the perpendicular bisector will pass through the mid point of the line segment which is (3, 2) and its equation will be x = 3.
Hence, any point with x-coordinate 3 will make an isosceles triangle.

Both (3, 6) and (3, -6) satisfy this condition.

Dear Mr. Anurag,

I think in real GMAT exam, there will be only one correct answer. What will we do if we face something like this, as both (3, 6) and (3, -6) are correct answer?

Cheers!