SAT Math Multiple Choice Question 707: Answer and Explanation
Note: Figure not drawn to scale.
In the figure above, AB = BC. If has a slope of m and has a slope of n, what is the value of mn?
- A. -9
- D. 9
Correct Answer: 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 and are opposites. We can calculate the slope of from its endpoints:
Therefore, the slope of is 3, and so mn = (3)(-3) = -9.