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# 18.Cydney is proving that perpendicular lines have slopes that are opposite reciprocals. She draws line p and labels two points on the line

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18.Cydney is proving that perpendicular lines have slopes that are opposite reciprocals. She draws line p and labels two points on the line as (0, a)(0, a) and (b, 0)(b, 0) .

Enter the answers, in simplest form, in the boxes to complete the proof.

The slope of line p is _____ . Rotate line p 90° counterclockwise about the origin to get line q. The labeled points on line p map

to (−a, 0)(−a, 0) and (___,___) on line q. The slope of line q is _____. The slopes of the lines are opposite reciprocals because

the product of the slopes is______ .

sii1lver  Jan 7, 2018
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Slope of p  =    -a/b

(0, b)  is on line  q

Slope of q  =  ( b - 0) / (0 - -a)  =   b/a

Product of the slopes  =  (-a/b) (b/a)  =  (-ab) /(ab)  =  -1

CPhill  Jan 7, 2018

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