a line has a slope of $-\frac{4}{5}$. which ordered pairs could be points on a line that is perpendicular to…

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.\n$(-2,0)$ and $(2,5)$\n$(-4,5)$ and $(4, - 5)$\n$(-3,4)$ and $(2,0)$\n$(1,-1)$ and $(6,-5)$\n$(2,-1)$ and $(10,9)$

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.\n$(-2,0)$ and $(2,5)$\n$(-4,5)$ and $(4, - 5)$\n$(-3,4)$ and $(2,0)$\n$(1,-1)$ and $(6,-5)$\n$(2,-1)$ and $(10,9)$

Answer

Explanation:

Step1: Find slope of perpendicular line

The slope of a line perpendicular to a line with slope $m$ is the negative - reciprocal. Given $m =-\frac{4}{5}$, the slope of the perpendicular line is $\frac{5}{4}$.

Step2: Use slope formula for each pair

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For $(-2,0)$ and $(2,5)$: $m=\frac{5 - 0}{2-(-2)}=\frac{5}{4}$. For $(-4,5)$ and $(4,-5)$: $m=\frac{-5 - 5}{4-(-4)}=\frac{-10}{8}=-\frac{5}{4}$. For $(-3,4)$ and $(2,0)$: $m=\frac{0 - 4}{2-(-3)}=\frac{-4}{5}$. For $(1,-1)$ and $(6,-5)$: $m=\frac{-5+1}{6 - 1}=\frac{-4}{5}$. For $(2,-1)$ and $(10,9)$: $m=\frac{9 + 1}{10 - 2}=\frac{10}{8}=\frac{5}{4}$.

Answer:

$(-2,0)$ and $(2,5)$; $(2,-1)$ and $(10,9)$