Question

PLEASE HELP!
Find the equation of the perpendicular bisector of the segment AB, if A(2, 2) and B(4, −6). If the perpendicular bisector of AB intercepts the y-axis at point P, what are the lengths of PA and PB?

Answer 1

Answer:

PLS FOLLOW ME

MARK AS BRAINLIST

GIVE THNX PLSSSSSSSS

Step-by-step explanation:

step 1

Find the midpoint AB (because a bisector divide into two equal parts)

we have

A(3, 0) and B(–1, 2)

step 2

Find the slope AB

we have

A(3, 0) and B(–1, 2)

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

substitute the values

step 3

Find the slope of the perpendicular bisector of the segment AB

Remember that

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

m1*m2=-1

we have

so

step 4

Find the equation of the perpendicular bisector of the segment AB

we have

-----> midpoint AB

substitute

Convert to slope intercept form

step 5

Find the x-intercept (point P)

For y=0

0=2x-1

2x=1

x=0.5

The x-intercept is the point P(0.5,0)

step 6

Find the length PA

we have

P(0.5,0),A(3,0)

the formula to calculate the distance between two points is equal to

substitute the values

step 7

Find the length PB

we have

P(0.5,0),B(-1,2)

the formula to calculate the distance between two points is equal to

substitute the values