Question

Determine the missing information in the paragraph proof.

Given: Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular. Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).


Prove: The slopes of perpendicular lines are negative reciprocals.



The slopes of lines PQ and P’Q’ can be determined using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction


The product of these slopes is ________. This product shows that the slopes are negative reciprocals. It is given that the lines are perpendicular and we have shown that the slopes of the lines are negative reciprocals.

Answer 1

a

Explanation:

took the test today

Answer 2

A)
`((d-b)/(c-a) )((c-a)/(-d+b) )`

The product of these slopes is -1

Explanation:

The slope of perpendicular lines are negative reciprocal.This means that when you multiply the two slopes you get -1.

To find slope of a line you apply;

m=change is y-axis values/change in x-axis values

Given that there are two lines, PQ and P'Q' then to find slope you follow;

Line PQ where P(a,b) and Q (c,d) slope,m= (d-b / c-a )

Line P'Q' where P'(-b,a) and Q'(-d,c) slope , m= ( c-a / -d+b)

Multiplying the two slopes

`(d-b)/(c-a) *(c-a)/(-d+b) \\\\\\(d-b)/(-d+b) \\\\=-1`