Answer:
The slope of line m is (-b/a).
The labelled points on line m map to (0,-a) and (b,0) on the line n.
The slope of line n is (a/b).
The slopes of the lines are opposite reciprocals because the product of the slopes is -1.
Step-by-step explanation:
The slope of a line connecting the points (x₁,y₁) and (x₂,y₂) is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of line m is
[tex]m_{1} = \frac{b-0}{0-a} = - \frac{b}{a}[/tex]
The line is rotated clockwise by an angle 90° to get line n.
The coordinates of the line n are (0,-a) and (b,0)
The slope of line n is
[tex]m_{2} = \frac{0+a}{b-0} =\frac{a}{b}[/tex]
We see that,
m₁m₂ = -(b/a) * (a/b) = -1
Hence the products of the slopes of perpendicular lines is -1.
