Question

The line L1 passes through the points (1, 7) and (3, 13) and L2 passes through the points (-2, 4) and (1, 3). L1 and L2 are:

Answer 1

First, we need to determine their slopes

Let m1 be the slope for L1 and m2 be the slope for L2.

If m1 = m2 then the lines are parallel and if m1 = - 1 /m2 , then the lines are perpendicular.

We can find the slopes using the formula below:

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

For L1

(1, 7) and (3, 13)

x₁=1 y₁=7 x₂=3 y₂=13

substitute the values into the formula and evaluate

`m_1=(13-7)/(3-1)=(6)/(2)=3`

For L2

(-2, 4) and (1, 3)

x₁=-2 y₁=4 x₂=1 y₂=3

substitute the values into the formula and evaluate

`m_2=(3-4)/(1+2)=-(1)/(3)`

Since m1 = 1 /m2, then the L1 and L2 are perpendicular.