Question

Which point could be on the line that is perpendicular to and passes through point K?

Answer 1

(2, 2)

Explanation:

First we find the slope of the line through M and N. The coordinates of M are (2, 3) and the coordinates of N are (-3, 2). Using the formula for slope,

`m=(y_2-y_1)/(x_2-x_1)=(3-2)/(2--3)=(1)/(5)`

For a line to be perpendicular to a given line, the slopes would be negative reciprocals (opposite signs and the fraction is flipped). This makes the slope of the perpendicular line -5/1.

The coordinates of point K are (3, -3). Going down 5 units and right 1 unit would put it at (4, -8). Going backwards, up 5 units and left 1 unit would be (2, 2). Thus (2, 2) is the point we are looking for.

Answer 2

It would be (2,2), because of the opposite reciprocal slope of a perpendicular line.