SAT Math Multiple Choice Question 672: Answer and Explanation
Note: Figure not drawn to scale.
In the figure above, if m || l, what is the area, in square units, of the shaded rectangle?
- A. 156
- B. 168
- C. 180
- D. 192
Correct Answer: D
Special Topics (coordinate geometry) MEDIUM
First, find the slope of l using the points (0, -9) and (12, 0):
Since the two lines are parallel, line m must also have a slope of . Now we can solve for k using the slope equation and the two points on line m, (0, 0) and (k, 12):
4(12) = 3(k)
48 = 3k
Divide by 3:
16 = k
Notice that the coordinates of the point (16, 12) correspond to the width and the length of the rectangle, respectively. Therefore, the area of the rectangle is 16 × 12 = 192 square units.