Question

Which of the following coordinates for P will make line MN perpendicular to line OP in the diagram below?%0D%0A%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(–2, –5)%0D%0A(–2, –5)%0D%0A%0D%0A(–3, 6)%0D%0A(–3, 6)%0D%0A%0D%0A(3, 2)%0D%0A(3, 2)%0D%0A%0D%0A(3, 5)

Answer 1

To determine which coordinates for P will make line MN perpendicular to line OP, we need to consider the slopes of the two lines.

The slope of line MN is equal to the reciprocal of the slope of line OP for the lines to be perpendicular.

Looking at the diagram, we can determine the coordinates of points M and N.

From the diagram, point M is located at (3, 2) and point N is located at (3, 5).

The slope of line MN can be determined by finding the difference in y-coordinates over the difference in x-coordinates, or (5 - 2) / (3 - 3) which equals 3/0.

However, this is undefined since we are dividing by zero. Therefore, the slope of line MN is undefined.

For line OP to be perpendicular to line MN, the slope of line OP must be the negative reciprocal of the undefined slope of line MN.

Since the undefined slope of line MN is undefined, its negative reciprocal does not exist.

Therefore, none of the given coordinates for P will make line MN perpendicular to line OP.