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:

$\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}$

For L1

(1, 7) and (3, 13)

x₁=1 y₁=7 x₂=3 y₂=13

substitute the values into the formula and evaluate

$m_1=\frac{13-7}{3-1}=\frac{6}{2}=3$

For L2

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

x₁=-2 y₁=4 x₂=1 y₂=3

substitute the values into the formula and evaluate

$m_2=\frac{3-4}{1+2}=-\frac{1}{3}$

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