Question

Find the midpoint of pq with endpoints p(-7,0) and q(1,8). then write an equation of the line that passes through the midpoint and is perpendicular to pq.

Answer 1

`y=-x+1`

Explanation:

`midpoint=((x_1+x_2)/(2) ,(y_1+y_2)/(2) )`

Find the midpoint:

`M=((-7+1)/(2) ,(0+8)/(2) )=(-3,4)`

`slope=(rise)/(run) =(y_2-y_1)/(x_2-x_1)`

Find the slope:

`m=(8-0)/(1--7) =(8)/(8) =1`

Perpendicular lines have negative reciprocal slopes, therefore:

`m=-1`

Use the point-slope formula with our new slope and midpoint:

`(y-4)=-1(x+3)`

Distribute -1:

`(y-4)=-x-3`

Add 4 to both sides:

`y=-x+1`