Given ghi g (4,-3), h (-4,2), and i (2,4), find the perpendicular bisector of hi in standard form.

Step-by-step explanation:

step 1

Find the slope of segment HI

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

we have

H (-4,2), and I (2,4)

substitute the given points

simplify

step 2

Find the slope of the perpendicular line to segment HI

we know that

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

we have

so

step 3

Find the midpoint segment HI

we know that

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

we have

H (-4,2), and I (2,4)

substitute

step 4

we know that

The perpendicular bisector of HI is a line perpendicular to HI that passes though the midpoint of HI

Find the equation of the perpendicular bisector of HI in point slope form

we have

substitute

step 5

Convert to slope intercept form

Isolate the variable y

step 6

Convert to standard form

where

A is a positive integer

B and C are integers

Adds 3x both sides

see the attached figure to better understand the problem

answer:   y=2x-3

step-by-step explanation: