# Line QR contains (2, 8) and (3, 10) Line ST contains points (0, 6) and (-2,2). Are lines QR and ST parallel or perpendicular?

Jan 13, 2017

Lines are parallel.

#### Explanation:

For finding whether lines $Q R$ and $S T$ are parallel or perpendicular, what we need is ti find their slopes.

If slopes are equal , lines are parallel and if product of slopes is $- 1$, they are perpendicular .

The slope of a line joining points $\left({x}_{1} , {y}_{1}\right)$ and x_2,y_2) is $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

Hence slope of $Q R$ is $\frac{10 - 8}{3 - 2} = \frac{2}{1} = 2$

and slope of $S T$ is $\frac{2 - 6}{- 2 - 0} = \frac{- 4}{- 2} = 2$

As the slopes are equal, lines are parallel.
graph{(y-2x-4)(y-2x-6)=0 [-9.66, 10.34, -0.64, 9.36]}