we know that
if two lines are perpendicular
then the product of their slopes is equal to minus one
so
![m1*m2=-1](https://tex.z-dn.net/?f=m1%2Am2%3D-1)
in this problem we have
![m1=-\frac{4}{5}](https://tex.z-dn.net/?f=m1%3D-%5Cfrac%7B4%7D%7B5%7D)
the value of m2 must be equal to
![m2=-\frac{1}{m1} =-\frac{1}{(-4/5)}=\frac{5}{4}](https://tex.z-dn.net/?f=m2%3D-%5Cfrac%7B1%7D%7Bm1%7D%20%3D-%5Cfrac%7B1%7D%7B%28-4%2F5%29%7D%3D%5Cfrac%7B5%7D%7B4%7D)
we know that
The formula to calculate the slope between two points is equal to
![m=\frac{(y2-y1)}{(x2-x1)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%28y2-y1%29%7D%7B%28x2-x1%29%7D)
<u>Find the slopes of each of ordered pairs and compare with m2</u>
<u>case a) </u>![(-2,0)\ and\ (2,5)](https://tex.z-dn.net/?f=%28-2%2C0%29%5C%20and%5C%20%282%2C5%29)
Substitute in the formula
![m=\frac{(5-0)}{(2+2)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%285-0%29%7D%7B%282%2B2%29%7D)
![m=\frac{(5)}{(4)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%285%29%7D%7B%284%29%7D)
The slope is equal to m2
so
The ordered pair case a) could be points on a line that is perpendicular to the given line
<u>case b) </u>![(-4,5)\ and\ (4,-5)](https://tex.z-dn.net/?f=%28-4%2C5%29%5C%20and%5C%20%284%2C-5%29)
Substitute in the formula
![m=\frac{(-5-5)}{(4+4)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%28-5-5%29%7D%7B%284%2B4%29%7D)
![m=\frac{(-10)}{(8)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%28-10%29%7D%7B%288%29%7D)
![m=-\frac{5}{4}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B5%7D%7B4%7D)
The slope is not equal to m2
so
The ordered pair case b) could not be points on a line that is perpendicular to the given line
<u>case c) </u>![(-3,4)\ and\ (2,0)](https://tex.z-dn.net/?f=%28-3%2C4%29%5C%20and%5C%20%282%2C0%29)
Substitute in the formula
![m=\frac{(0-4)}{(2+3)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%280-4%29%7D%7B%282%2B3%29%7D)
![m=\frac{(-4)}{(5)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%28-4%29%7D%7B%285%29%7D)
The slope is not equal to m2
so
The ordered pair case c) could not be points on a line that is perpendicular to the given line
<u>case d) </u>![(1,-1)\ and\ (6,-5)](https://tex.z-dn.net/?f=%281%2C-1%29%5C%20and%5C%20%286%2C-5%29)
Substitute in the formula
![m=\frac{(-5+1)}{(6-1)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%28-5%2B1%29%7D%7B%286-1%29%7D)
![m=\frac{(-4)}{(5)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%28-4%29%7D%7B%285%29%7D)
The slope is not equal to m2
so
The ordered pair case d) could not be points on a line that is perpendicular to the given line
<u>case e) </u>![(2,-1)\ and\ (10,9)](https://tex.z-dn.net/?f=%282%2C-1%29%5C%20and%5C%20%2810%2C9%29)
Substitute in the formula
![m=\frac{(9+1)}{(10-2)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%289%2B1%29%7D%7B%2810-2%29%7D)
![m=\frac{(10)}{(8)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%2810%29%7D%7B%288%29%7D)
![m=\frac{5}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B5%7D%7B4%7D)
The slope is equal to m2
so
The ordered pair case e) could be points on a line that is perpendicular to the given line
therefore
<u>the answer is</u>
![(-2,0)\ and\ (2,5)\\(2,-1)\ and\ (10,9)](https://tex.z-dn.net/?f=%28-2%2C0%29%5C%20and%5C%20%282%2C5%29%5C%5C%282%2C-1%29%5C%20and%5C%20%2810%2C9%29)