8. line contains points (p − 4, 2) and (−2, 9). line contains points (p, −1) and (−1, 1).
a. find the value of p if the lines are parallel.
b. find the value(s) of p if the lines are perpendicular.

Answer with Step-by-step explanation:

We are given that a line  passing through the point (p-4,2) and (-2,9) and other  line  passing through the point (p,-1) and (-1,1).

Slope-formula:

By using the formula

Slope of line which passing through the point (p-4,2) and (-2,9)

Slope of other line which passing through the point (p,-1) and (-1,1)

When two lines are parallel then their slopes are equal

a.

b.If the two lines are perpendicular then their slopes is opposite reciprocal to each other.

It is quadratic equation in variable p

The root of equation are imaginary which is not possible .

If the lines are perpendicular then the value of p does not exist.

step-by-step explanation:

options

the answer is b