Answer:
The lines L1 and L2 neither parallel nor perpendicular
Step-by-step explanation:
* Lets revise how to find a slope of a line
- If a line passes through points (x1 , y1) and (x2 , y2), then the slope
of the line is ![m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
- Parallel lines have same slopes
- Perpendicular lines have additive, multiplicative slopes
( the product of their slopes is -1)
* Lets solve the problem
∵ L1 passes through the point (1 , 10) and (-1 , 7)
- Let (1 , 10) is (x1 , y1) and (-1 , 7) is (x2 , y2)
∴ x1 = 1 , x2 = -1 and y1 = 10 , y2 = 7
∴ The slope of L1 is ![m1 = \frac{7-10}{-1-1}=\frac{-3}{-2}=\frac{3}{2}](https://tex.z-dn.net/?f=m1%20%3D%20%5Cfrac%7B7-10%7D%7B-1-1%7D%3D%5Cfrac%7B-3%7D%7B-2%7D%3D%5Cfrac%7B3%7D%7B2%7D)
∵ L2 passes through the point (0 , 3) and (1 , 5)
- Let (0 , 3) is (x1 , y1) and (1 , 5) is (x2 , y2)
∴ x1 = 0 , x2 = 1 and y1 = 3 , y2 = 5
∴ The slope of L2 is ![m2=\frac{5-3}{1-0}=\frac{2}{1}=2](https://tex.z-dn.net/?f=m2%3D%5Cfrac%7B5-3%7D%7B1-0%7D%3D%5Cfrac%7B2%7D%7B1%7D%3D2)
∵ m1 = 3/2 and m2 = 2
- The two lines have different slopes and their product not equal -1
∴ The lines L1 and L2 neither parallel nor perpendicular