Answer :
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 [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- 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 [tex]m1 = \frac{7-10}{-1-1}=\frac{-3}{-2}=\frac{3}{2}[/tex]
∵ 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 [tex]m2=\frac{5-3}{1-0}=\frac{2}{1}=2[/tex]
∵ 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
By calculating the slopes of L1 and L2, we find that they are 1.5 and 2 respectively. Since they are neither the same nor negative reciprocals, L1 and L2 are neither parallel nor perpendicular.
To determine if lines L1 and L2 are parallel, perpendicular, or neither, we need to calculate the slopes of both lines using the slope formula:
Slope formula: (y2 - y1) / (x2 - x1)
Calculating the slope of L1:
Points on L1: (1, 10) and (-1, 7)
Slope of L1 = (7 - 10) / (-1 - 1) = (-3) / (-2) = 1.5
Calculating the slope of L2:
Points on L2: (0, 3) and (1, 5)
Slope of L2 = (5 - 3) / (1 - 0) = 2 / 1 = 2
Since the slopes of L1 (1.5) and L2 (2) are neither the same nor negative reciprocals of each other, the lines L1 and L2 are neither parallel nor perpendicular.
