Question

Line A contains the points (2, 6) and (4, 10). Line B contains the

points (-2, 3) and (3, 13).
1. Are the lines parallel? Explain your reasoning.

Answer 1

Answer: lines are parallel

Explanation:

Lines are parallel if they have the same slope

`\boxed {The\ slope\ m=(y_2-y_1)/(x_2-x_1) }`

1) (2,6) (4,10)

x₁=2 x₂=4 y₁=6 y₂=10

Hence,

`\displaystyle\\m=(10-6)/(4-2) \\\\m=(4)/(2)\\\\m=2`

2) (-2,3) (3,13)

x₁=-2 x₂=3 y₁=3 y₂=13

Hence,

`\displaystyle\\m_1=(13-3)/(3-(-2)) \\\\m_1=(10)/(3+2) \\\\m_1=(10)/(5)\\\\m_1=2`

m=m₁=2

Hence, lines are parallel

Answer 2

It is not possible to determine whether the lines are parallel based on the information given. To determine whether two lines are parallel, we need to calculate the slope of each line and compare them. The slope is calculated as the change in the y-coordinate divided by the change in the x-coordinate, or (y2-y1)/(x2-x1). Since we only have the coordinates of the endpoints of the lines and not the equations of the lines, we cannot calculate the slope and therefore cannot determine whether the lines are parallel.