Question

The given line segment has a midpoint at (−1, −2).

Answer 1

Answer:

y = -4(x) - 6

Step-by-step explanation:

For anyone looking for a simple answer.

Answer 2

Answer:

The equation of the perpendicular line is y = −4(x) − 6

Step-by-step explanation:

Given:

Three coordinates points (in pair).

Lets choose two points,in $(x,y)$ format.

Where

$(x,y)$ = $(-5,-3)$ and $(x_1,y_1)$ = $(3,-1)$

From these points we will find the slope using point-slope formula.

That is :

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

$m=\frac{(y_1-y)}{(x_1-x)}$

Plugging the values:

$m=\frac{-1+3}{3+5}=\frac{1}{4}$

Now we know that product of slope of two perpendicular lines = -1.

So the slope of the line which is perpendicular $(m_1)$ .

$m_1=\frac{-1}{m}$

$m_1=\frac{-1}{\frac{1}{4} } =-1\times \frac{4}{1} =-4$

Now using this slope we will plug the midpoint (-1,-2) values in point-slope form and reduced it to slope intercept.

$y-(-2)=-4(x+1)$

$y+2=-4x-4$

$y=-4x-4-2$

$y=-4x-6$

So the equation of the perpendicular bisector is y = -4(x) - 6