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¯¯¯¯¯¯¯¯ . This line is called the perpendicular bisector. The midpoint is ( , ). The equation of the perpendicular bisector is y = .

Answer 1

Answer with Step-by-step explanation:

We are given that

P(-7,0) and Q(1,8)

We have to find the midpoint of PQ and write an equation of the line that passes through the midpoint.

Mid-point formula: $x=\frac{x_1+x_2}{2}, y=\frac{y_1+y_2}{2}$

By using this formula ,

The mid point of PQ

$x=\frac{-7+1}{2}=-3, y=\frac{0+8}{2}=4$

Hence, the midpoint of PQ is (-3,4).

Slope of PQ=$m=\frac{y_2-y_1}{x_2-x_1}=\frac{8-0}{1+7}=1$

Slope of perpendicular line=$\frac{-1}{slope\;of PQ}=-1$

The equation of line which is passing through the point (-3,4) with slope -1 is given by

$y-y_1=m(x-x_1)$

The equation of line which is passing through the point (-3,4) with slope -1 is given by

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

$y-4=-x-3$

$y=-x-3+4$

$y=-x+1$