Question

AB and BC form a right angle at point B if A = (-3,-1) and B = (4,4) what is the equation if BC

Answer 1

-7x − 5y = -48

Explanation:

This was correct on plato :D

Answer 2

`7x+5y-48=0`

Explanation:

Refer the attached figure .

We are given a line AB

Point A
`=(x_1,y_1) = (-3,-1)`

Point B
`=(x_2,y_2) = (4,4)`

Formula for slope 'm' when two points are given :

`m=(y_2-y_1)/(x_2-x_1)`

Substituting thew values

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

`m=(5)/(7)`

Since we are given that AB is perpendicular to BC

So, By property - perpendicular slopes are negative reciprocals of each other.

`\Rightarrow m_1* m_2 =-1`

`\Rightarrow (5)/(7)* m_2 =-1`

`\Rightarrow m_2 = (-7)/(5)`

So, Slope for line BC :
`m_2 = (-7)/(5)`

Point B = (4,4)

Formula of equation of line :
`y-y_1=m(x-x_1)`

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

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

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

`7x+5y-20-28=0`

`7x+5y-48=0`

Hence the equation of line BC :
`7x+5y-48=0`