Question

a line has a slope of $-\frac{4}{5}$. which ordered pairs could be points on a line that is perpendicular to this line? select two options.\
$(-2, 0)$ and $(2, 5)$\
$(-4, 5)$ and $(4, -5)$\
$(-3, 4)$ and $(2, 0)$\
$(1, -1)$ and $(6, -5)$\
$(2, -1)$ and $(10, 9)$

Explanation:

Step1: Find perpendicular slope

The slope of the given line is $-\frac{4}{5}$. Perpendicular slopes are negative reciprocals, so:
$$m_{\perp} = \frac{5}{4}$$

Step2: Calculate slope for pair 1

For $(-2, 0)$ and $(2, 5)$, use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$:
$$m=\frac{5-0}{2-(-2)}=\frac{5}{4}$$

Step3: Calculate slope for pair 2

For $(-4, 5)$ and $(4, -5)$:
$$m=\frac{-5-5}{4-(-4)}=\frac{-10}{8}=-\frac{5}{4}$$

Step4: Calculate slope for pair 3

For $(-3, 4)$ and $(2, 0)$:
$$m=\frac{0-4}{2-(-3)}=\frac{-4}{5}$$

Step5: Calculate slope for pair 4

For $(1, -1)$ and $(6, -5)$:
$$m=\frac{-5-(-1)}{6-1}=\frac{-4}{5}$$

Step6: Calculate slope for pair 5

For $(2, -1)$ and $(10, 9)$:
$$m=\frac{9-(-1)}{10-2}=\frac{10}{8}=\frac{5}{4}$$

Answer:

A. $(-2, 0)$ and $(2, 5)$
E. $(2, -1)$ and $(10, 9)$