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.

A)

The product of these slopes is -1

Step-by-step 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

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47