Question

Consider the line in the coordinate plane that passes through the point (-5, 2) and the origin. Find the slope of a line perpendicular to the line described;

What is the best description for the lines?
a) 2/5
b) -5/2
c) -5
d) 5/2

Answer 1

The slope of the line perpendicular to the line passing through (-5, 2) and the origin is 5/2, which is the negative reciprocal of the original line's slope of -2/5.

Step-by-step explanation:

To find the slope of a line perpendicular to the line that passes through the point (-5, 2) and the origin (0,0), we first need to calculate the slope of the given line. The slope (m) is defined as the rise divided by the run. In this case, the rise is the difference in the y-coordinates (2 - 0), and the run is the difference in the x-coordinates (-5 - 0). So the slope of the line through (-5, 2) and the origin is:

m = (2 - 0) / (-5 - 0) = 2 / -5 = -2/5.

For a line to be perpendicular to another, its slope must be the negative reciprocal of the original line's slope. So the slope of the perpendicular line would be:

m = -1 / (-2/5) = 5/2.

Therefore, the correct answer is (d) 5/2. Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. In this case, since the original line has a negative slope, the perpendicular line will have a positive slope and vice versa.