2017 AMC 10B Problem 8

Problem 8 of 25EasierGeometry

Points

A(11, 9)

and

B(2, -3)

are vertices of

\triangle ABC

with

AB=AC.

The altitude from

A

meets the opposite side at

D(-1, 3).

What are the coordinates of point

C?

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Solution

Since

AB=AC,

the altitude from

A

also bisects the base

BC.

Therefore,

D

is the midpoint of

BC.

C=(x,y),

then we have

\frac{x+2}2 = -1,

\frac{y-3}2=3.

As such,

C=(x,y)=(-4,9).

Thus, the correct answer is C .

Concepts: coordinate geometry · midpoint · isosceles triangle

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.