Question

Are these lines perpendicular?While these lines mayappear to intersect at a 90°angle, it is best to find theirslopes to make sure.Orange line[?]runSlope = rise=Hint: First enter therise, or change in y-value, of the orangeline.

Answer 1

Answer

The lines are NOT perpendicular.

Explanation

The slope of the orange line is given as follows:

$\text{Slope }=\frac{rise}{run}=\frac{\Delta y}{\Delta x}=\frac{2-0}{3-0}=\frac{2}{3}$

Similarly, the slope of the blue line is given as follows:

$\text{Slope }=\frac{rise}{run}=\frac{\Delta y}{\Delta x}=\frac{0-2}{0--1}=\frac{-2}{1}=-2$

For these lines to be perpendicular, the product of the two slopes must be equal to -1.

The product of the two slopes =

$\begin{gathered} \frac{2}{3}\times-2=-\frac{4}{3} \\ -\frac{4}{3}\ne-1 \end{gathered}$

Hence, the lines are NOT perpendicular.