Question

Select the slope perpendicular to (2,9) (1,5)

a
-1/4

b
4

c
2/3

d
-3/2

Answer 1

To find the slope perpendicular to the line defined by the points (2, 9) and (1, 5), we first need to calculate the slope of the line connecting these two points.

The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Plugging in the coordinates (2, 9) as \((x_1, y_1)\) and (1, 5) as \((x_2, y_2)\):

\[
m = \frac{5 - 9}{1 - 2} = \frac{-4}{-1} = 4
\]

Now that we have the slope of the line as 4, the slope of the line that is perpendicular to this line is the negative reciprocal of 4.

To find the negative reciprocal:

1. Take the reciprocal: \( \frac{1}{4} \)
2. Change the sign: \( -\frac{1}{4} \)

Therefore, the slope perpendicular to the slope of 4 is:

\[
-\frac{1}{4}
\]

So, the answer is:

a. \(-\frac{1}{4}\)