Question

Ab and bc form a right angle at point B. if a= (-3,-1) and B= (4,4) what is the equation of BC?

Answer 1

Option C
`-7x-5y=-48`

Explanation:

step 1

Find the slope of AB

we have

A(-3,-1) and B(4,4)

The slope m is equal to

`m=(4+1)/(4+3)`

`m=5/7`

step 2

Find the slope of BC

we know that

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

so

`m1*m2=-1`

we have

`m1=5/7`

substitute

`5/7*m2=-1`

`m2=-7/5`

step 3

Find the equation of the line into slope point form

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

we have

`m=-7/5`

`B(4,4)`

substitute

`y-4=-(7/5)(x-4)`

Multiply by 5 both sides

`5y-20=-7x+28`

`7x+5y=28+20`

`7x+5y=48`

Multiply by -1 both sides

`-7x-5y=-48`