Question

Which ordered pairs could be points on a line that is perpendicular to a line with a slope of -4/5?

A. (-2,0) and (2,5)
B. (-4,5) and (4,-5)
C. (-3,4) and (2,0)
D. (1,-1) and (6,-5)
E. (2,-1) and (10,9)

Answer 1

The correct ordered pairs that could be points on a line perpendicular to a line with a slope of -4/5 is option A. This is determined by finding the slope between the given points and confirming that it is the negative reciprocal of -4/5, which is 5/4.

Step-by-step explanation:

The student's question asks about identifying which ordered pairs could form a line perpendicular to a line with a slope of -4/5. When two lines are perpendicular, their slopes are negative reciprocals of each other. The negative reciprocal of -4/5 is 5/4. Therefore, we must find which pair of points would have a slope of 5/4.

Firstly, we calculate the slope between the given points using the slope formula m = (y2 - y1) / (x2 - x1). For option A, the slope is (5 - 0) / (2 - (-2)) = 5/4, so option A's points could indeed be on a line that is perpendicular to a line with a slope of -4/5.

Checking the other options in the same manner will show that none of the other pairs of points yield a slope of 5/4, thus option A is the correct one.