Question

Which of the following points could lie on the line perpendicular to a line with a slope of -1 passing through the point (2, -2)?

a) (3, 1)
b) (-2, 1)
c) (0, -1)
d) (-4, -3)

Answer 1

The point (-4, -3) lies on the line perpendicular to a line with a slope of -1 passing through the point (2, -2).

Step-by-step explanation:

We know that the line perpendicular to a line with a slope of -1 will have a slope which is the negative reciprocal of the slope of the original line. The original line has a slope of -1, so the perpendicular line will have a slope of 1.

Using the point-slope form of a linear equation, we can write the equation of the line that is perpendicular to the original line and passes through the point (2, -2) as: y - (-2) = 1(x - 2)

Simplifying the equation, we get: y + 2 = x - 2

So, the equation of the perpendicular line is y = x - 4. To determine which points could lie on this line, we can substitute the x and y values of each point into the equation and see if it satisfies the equation.

1. For point (3, 1): Substitute x = 3 and y = 1 in the equation: 1 = 3 - 4 which is not true.
2. For point (-2, 1): Substitute x = -2 and y = 1 in the equation: 1 = -2 - 4 which is not true.
3. For point (0, -1): Substitute x = 0 and y = -1 in the equation: -1 = 0 - 4 which is not true.
4. For point (-4, -3): Substitute x = -4 and y = -3 in the equation: -3 = -4 - 4 which is true.

Therefore, the point (-4, -3) lies on the line perpendicular to a line with a slope of -1 passing through the point (2, -2).