Answer:
(-6,-8),(7,18) and (-4,6),(2,3) lie on perpendicular lines
Step-by-step explanation:
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%7By2-y1%7D%7Bx2-x1%7D)
step 1
Find the slope of the pair (-6,-8),(7,18)
substitute
![m=\frac{18+8}{7+6}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B18%2B8%7D%7B7%2B6%7D)
![m=\frac{26}{13}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B26%7D%7B13%7D)
![m=2](https://tex.z-dn.net/?f=m%3D2)
step 2
Find the slope of the pair (6,4),(4,12)
substitute
![m=\frac{12-4}{4-6}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B12-4%7D%7B4-6%7D)
![m=\frac{8}{-2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B8%7D%7B-2%7D)
![m=-4](https://tex.z-dn.net/?f=m%3D-4)
step 3
Find the slope of the pair (-4,6),(2,3)
substitute
![m=\frac{3-6}{2+4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B3-6%7D%7B2%2B4%7D)
![m=\frac{-3}{6}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-3%7D%7B6%7D)
![m=-\frac{1}{2}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B1%7D%7B2%7D)
step 4
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
In this problem
and
are opposite reciprocal
therefore
(-6,-8),(7,18) and (-4,6),(2,3) lie on perpendicular lines