Question

For the given line segment, write the equation of the perpendicular bisector.

Answer 1

Answer:

$y=-0.8x-4.7$

Step-by-step explanation:

Let

$A(-6,-4), B(-2,1)$

we know that

The perpendicular bisector pass through the midpoint of AB

step 1

Find the midpoint AB

$M=((-6-2)/2,(-4+1)/2)$

$M=(-4,-1.5)$

step 2

Find the slope of the given line AB

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{1+4}{-2+6}$

$m=\frac{5}{4}$

step 3

Find the slope of the perpendicular bisector

we know that

If two lines are perpendicular, then  the product of their slopes is equal to -1

$m1*m2=-1$

we have

$m1=\frac{5}{4}$  ----> slope of the given line

substitute in the formula

$\frac{5}{4}*m2=-1$

$m2=-\frac{4}{5}=-0.8$

step 4

Find the equation of the perpendicular bisector

we know that

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

we have

$m=-0.8$

$M=(-4,-1.5)$

substitute

$y+1.5=-0.8(x+4)$

$y=-0.8x-3.2-1.5$

$y=-0.8x-4.7$