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Natasha_Volkova [10]
2 years ago
11

Two points on L1 and two points on L2 are given. Use the slope formula to determine if lines L1 and L2 are parallel, perpendicul

ar, or neither.
L1: (1, 10) and (-1, 7)
L2: (0, 3) and (1, 5 )
Mathematics
1 answer:
vlada-n [284]2 years ago
7 0

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}}

- 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}

∵ 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

∵ 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

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