Question

A is the point (-2,0)
B is the point (0,4)
C is the point (5,-1)

Find an equation of the line that passes through C and is perpendicular to AB

Answer 1

Answer:

y = 1/2x - 3.5

Step-by-step explanation:

so lets start by finding the equation of the line AB

we know the y-intercept is 4 from the point 0,4 so we know it'll look something like this

y = mx + 4 and we can plug in the other point we know -> 0 = m(-2) + 4  -> 4 = m(-2) -> m = -2 so the full equation of the line is y = -2x + 4

ok now we can find the other line. we know that perpendicular lines have an opposire reciprocal slope so in this case -2 would turn into 1/2

y = 1/2x + b

now lets plug in point C

-1 = (1/2)(5) + b

-1 - (2.5) = b

-3.5 = b

so the equation is y = 1/2x - 3.5

Answer 2

Answer:

$y=-\dfrac12 x + \dfrac32$

Step-by-step explanation:

Equation of line AB:

Let A = $(x_1,y_1)$ = (-2, 0)

Let B = $(x_2, y_2)$ = (0, 4)

Use equation of slope to find slope m:

$m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4 -0}{0+2}=2$

Use point-slope form for linear equation:

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

$\implies y-0=2(x+2)$

$\implies y =2x+4$

Equation of line passing through C

If the line that passes through C is perpendicular to AB, then their slopes will be opposite reciprocals of each other.

⇒ $m=\dfrac{-1}{2}=-\dfrac12$

Use point-slope form for linear equation and $(x_1,y_1)$ is point C:

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

$\implies y+1=-\dfrac12 (x-5)$

$\implies y=-\dfrac12 x + \dfrac32$