Question

Which of the following coordinates for P will make line MN perpendicular to line OP in the diagram below? (1 point) Responses (–2, –5) (–2, –5) (–3, 6) (–3, 6) (3, 2) (3, 2) (3, 5)

Answer 1

In order for line MN to be perpendicular to line OP, the product of their slopes should be -1.

The slope of line MN can be found by calculating the difference in y-coordinates divided by the difference in x-coordinates of two points on the line. Let's take the points P(-2, -5) and N(-3, 6):

slope of MN = (6 - (-5))/(-3 - (-2))
= (6 + 5)/(-3 + 2)
= 11/(-1)
= -11

Next, we need to calculate the slope of line OP. Let's take the points O(0, 0) and P(3, 5):

slope of OP = (5 - 0)/(3 - 0)
= 5/3

Since the product of the slopes of line MN and line OP is not -1, none of the given coordinates for P will make line MN perpendicular to line OP.