2017 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 8 Easy

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? (2017 AMC 10B Problem, Question#8)

  • A.

    (-8,9)

  • B.

    (-4,8)

  • C.

    (-4,9)

  • D.

    (-2,3)

  • E.

    (-1,0)

Answer:C

Since AB=AC, then \triangle ABC is isosceles, so BD=CD. Therefore, the coordinates of C are (-1-3,3+6)=(-4,9).

Calculating the equation of the line running between points B and D, y=-2x+1. The only coordinate of C that is also on this line is (-4,9).

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