Bunuel wrote:

What are the coordinates of point B in the xy-plane above ?

(A) (6, 12)

(B) (6, 28)

(C) (8, 20)

(D) (12, 20)

(E) (14, 28)

Attachment:

Untitled-1.jpg

Given (AB = BC): This triangle is isosceles.

The altitude, BD, of an isosceles triangle is a perpendicular bisector of the opposite side, which creates two congruent right triangles with equal bases, AD and DC.

Because the altitude is both perpendicular and a bisector, the x-coordinate of D also will be the x-coordinate of B.

To find the x-coordinate of D, and hence of vertex B, use midpoint formula:

\(\frac{x_1 + x_2}{2}=\frac{-8 + 20}{2}=\frac{12}{2}=\)

6To find y-coordinate of vertex B, use given information that AC = BD. To find

distance between two points that lie on the same line (y = 0), subtract x-coordinates of A and C*:

20 - (-8) = (20 + 8) = 28 = AC

AC = BD = 28. B's y-coordinate =

28B = (6,28)

Answer B

*

You also can just "count": From -8 to 0 = distance of 8. From 0 to 20 = distance of 20. (8 + 20) = 28
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