Question

100 points! Please help Mhanifa. Write an equation of the perpendicular bisector of the segment with the endpoints G(3,7) and H(-1,-5). I will mark brainliest!

Answer 1

Answer:

$y = - \frac{1}{3} x + \frac{4}{3}$

Step-by-step explanation:

We want to find the equation of the perpendicular bisector of the segment with the endpoints G(3,7) and H(-1,-5).

Since the line is a bisector, it means that it passes through the midpoint of G and H.

Also, since it is perpendicular to the line with endpoints G and H, it means that the slope is the negative inverse of the slope of the line between the two points.

First, find the midpoint of the two points G and H:

$m = ( \frac{x1 + x2}{2} \: \frac{y1 + y2}{2} ) \\ m = ( \frac{3 + ( - 1)}{2} \: \frac{7 + ( - 5)}{2} ) \\ m = (\frac{2}{2} \: \frac{2}{2} ) \\ m = (1. \: 1)$

Next, find the slope of the line between point G and H:

$m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{ - 5 - 7}{ - 1 - 3} = \frac{ - 12}{ - 4} \\ m = 3$

Now, find the negative inverse;

$m2 = - \frac{1}{m1} = - \frac{1}{3}$

Find the equation of the line using the point-slope method:

$y - y1 = m(x - x1) \\ y - 1 = - \frac{1}{3} (x - 1) \\ y - 1 = - \frac{1}{3} x + \frac{1}{3} \\ y = - \frac{1}{3} x + \frac{1}{3} + 1 \\ y = - \frac{1}{3} x + \frac{4}{3}$

That is the equation of the line.

Answer 2

Answer:

• y = -1/3x + 4/3

Step-by-step explanation:

Perpendicular bisector is the line with opposite-reciprocal slope and passes through the midpoint

The slope of GH is:

• m = (-5 - 7)/(-1 - 3) = -12/-4 = 3

Perpendicular line has slope:

• -1/m = -1/3

Midpoint of GH is:

• x = (3 - 1)/2 = 2/2 = 1
• y = (7 - 5)/2 = 2/2 = 1

The line with the slope of -1/3 and passes through point (1, 1) is:

• y - 1 = -1/3(x - 1) in point-slope form

And

• y = -1/3x + 4/3 in slope-intercept form