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

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

its A

Explanation:

Answer 2

The information given is sufficient for this proof .

Slope of a line passing through x1 ,y1) and ( x2,y2) is given by the formula :

M = ( y2 - y1)/ ( x2-x1)

________________________________

Let us start finding the slope of line PQ

the given points are ( a,b) and ( c,d)

using the slope formula we get :

slope of line PQ = m= ( d-b) /( c-a)

Let us now try finidng slope of the another line P'Q'

It is passing through ( -b ,a) and (-d,c)

using the formula we get slope of P'Q' = m' = ( c-a) /( -d - -b)

m'= ( c-a) /( -d+b)

m'= ( c-a) / -( b-d Let us find the product of m and m' :

( d-b ) * ( c-a)

----------- ------------ = -1

(c-a) - ( b-d)

Because we got product of m and m' = -1 hence proved product of perpendicular lines are negative reciprocal of each other .