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

-7x − 5y = -48

Explanation:

This was correct on plato :D

Answer 2

With fractions:
`y=-(7)/(5) x+(48)/(5)`

With decimals:
`y=-1.4x+9.6`

Explanation:

First we are finding the slope of line AB using the slope formula:

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

where

`m` is the slope

`(x_1,y_1)` are the coordinates of the first point

`(x_2,y_2)` are the coordinates of the second point

The first point is A= (-3, -1) and the second one is B = (4, 4), so
`x_1=-3`,
`y_1=-1`,
`x_2=4` and
`y_2=4`.

Replacing values

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

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

`m=(5)/(7)`

Now, since AB and BC form a right angle, BC is perpendicular to AB. The slope of a perpendicular line is the negative reciprocal of the other line; in other words, the slope of BC is the negative reciprocal of the slope of AB. To find the negative reciprocal of the slope of AB we just need to multiply its slope by -1 and invert the fraction:

`m_(AB)=(5)/(7)`

`m_(BC)=-(7)/(5)`

Finally, to complete the equation of BC, we are using the point-slope formula:

`y-y_1=m(x-x_1)`

where

`m` is the slope

`(x_1,y_1)` are the coordinates of the point

We know that
`m_(BC)=-(7)/(5)`, so
`m=-(7)/(5)`. Since the line passes throughout point B = (4, 4),
`x_1=4` and
`y_1=4`.

Replacing values

`y-y_1=m(x-x_1)`

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

`y-4=-(7)/(5) x+(28)/(5)`

`y=-(7)/(5) x+(28)/(5)+4`

`y=-(7)/(5) x+(48)/(5)`

`y=-1.4x+9.6`