Find the equation of the perpendicular bisector of the segment ab, if a(3, 0) and b(–1, 2). if the perpendicular bisector of ab intercepts the x-axis at point p, what are the lengths of pa and pb?

Part 1) The equation of the perpendicular bisector of the segment AB is

 or  

Part 2)

Part 3)

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

go and ask your mom to you