Devante is proving that perpendicular lines have slopes that are opposite reciprocals. he draws line m and labels two points on the line as (a, 0) and (0, b) . enter the answers, in simplest form, in the boxes to complete the proof. the slope of line m is . rotate line m 90° clockwise about the origin to get line n. the labeled points on line m map to (0, −a) and (, ) on line n. the slope of line n is . the slopes of the lines are opposite reciprocals because the product of the slopes is .

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

The slope of line m is

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

We see that,

m₁m₂ = -(b/a) * (a/b) = -1

Hence the products of the slopes of perpendicular lines is -1.

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