SAT Math Multiple Choice Question 707: Answer and Explanation

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Question: 707

2. Images

Note: Figure not drawn to scale.

In the figure above, AB = BC. If Images has a slope of m and Images has a slope of n, what is the value of mn?

  • A. -9
  • B. Images
  • C. Images
  • D. 9

Correct Answer: A

Explanation:

A

Algebra (slopes) MEDIUM

If AB = BC, then triangle ABC is isosceles and therefore the two base angles are congruent and the triangle has a vertical axis of symmetry at the line x = 3. This implies that the slopes of lines Images and Images are opposites. We can calculate the slope of Images from its endpoints:

Images

Therefore, the slope of Images is 3, and so mn = (3)(-3) = -9.

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