Answer:
The two lines are not perpendicular because the product of their slopes is not equal to -1
Step-by-step explanation:
The product of the slopes of the perpendicular line is -1
- That means one of them is and additive and multiplicative inverse of the other
- If the slope of one of them is m, then reciprocal m and change its sign, then the slope of the perpendicular is [tex]-\frac{1}{m}[/tex]
- The formula of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let us find from the graph two points lie on each line and calculate the slopes of them and then find its product if the product is -1, then the two lines are perpendicular
From the graph
∵ The red line passes through points (4 , 0) and (0 , 8)
∴ [tex]x_{1}[/tex] = 4 and [tex]x_{2}[/tex] = 0
∴ [tex]y_{1}[/tex] = 0 and [tex]y_{2}[/tex] = 8
∵ [tex]m=\frac{8-0}{0-4}=\frac{8}{-4}=-2[/tex]
∴ The slope of the red line is -2
∵ The blue line passes through points (5 , 5) and (0 , -5)
∴ [tex]x_{1}[/tex] = 5 and [tex]x_{2}[/tex] = 0
∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = -5
∵ [tex]m=\frac{-5-5}{0-5}=\frac{-10}{-5}=2[/tex]
∴ The slope of the blue line is 2
∵ The products of the slopes of the two lines = -2 × 2 = -4
∴ The product of the slopes of the lines not equal -1
∴ The two lines are not perpendicular
