Write the equation for the perpendicular bisector of the given line segment.
a
b)
4.3x+ /
= 3x }

Step-by-step explanation:

Let

A(-5,5),B(-2,-4) ----> the given segment

step 1

Find the slope AB

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

substitute the given values

step 2

we know that      

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

so

the slope of the perpendicular bisector is equal to

we have

substitute

step 3

Find the midpoint segment AB

A(-5,5),B(-2,-4)

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

substitute the values

step 4

Find the equation of the line in point slope form

we have

substitute

step 5

Convert to slope intercept form

isolate the variable y

simplify

see the attached figure to better understand the problem

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b