Co-ordinate geometry

pareekbharat86 wrote:What are the coordinates of point B in the xy-plane below?
(A) (6, 12)
(B) (6, 28)
(C) (8, 20)
(D) (12, 20)
(E) (14, 28)

If AB= BC, then ∆ABC is an ISOSCELES triangle, which mean that BD (the altitude) is also a perpendicular BISECTOR.
If BD bisects AC, then AD = DC
Since AC = 28, we know that AD = DC = 14, which means point D has coordinates (6, 0), which means point B has coordinates (6, ?)

At this point, we can eliminate answer choices C, D and E.
This means that the length of BD is either 12 or 28

IMPORTANT: In official GMAT Problem Solving questions, the given diagrams are drawn to scale unless it is stated otherwise. To learn more about this, you can watch this free video: https://www.gmatprepnow.com/module/gmat-geometry?id=863

So, if this were an official GMAT question, then we could probably just "eyeball" the diagram and determine whether BD has length 12 or 28. This diagram, however, is obviously not drawn to scale, so there should be some wording added to indicate this.

To determine the length of BD, we'll use the fact that BD = AC
Since AC has length 28, we know that BD has length 28, which means point B has coordinates [spoiler](6, 28)[/spoiler]

Answer: B

Cheers,
Brent