Question

Write the equation of the perpendicular bisector of the segment AB. A (1, 5) and B (7, -1)

Answer 1

Answer:

The equation of the perpendicular bisector of the segment AB is $y = x - 2$

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

$y = mx + b$

In which m is the slope and b is the y-intercept.

Perpendicular lines and slopes:

If two lines are perpendicular, the multiplication of their slopes is -1.

Equation of the perpendicular bisector of the segment AB.

Equation of a line that passes through the midpoint of segment AB and is perpendicular to AB.

Midpoint of segment AB:

Mean of their coordinates x and y. So

(1+7)/2 = 4

(5-1)/2 = 2

So (4,2).

Slope of segment AB:

When we have two points, the slope between them is given by the change in y divided by the change in x.

In segment AB, we have points (1,5) and (7,-1). So

Change in y: -1 - 5 = -6

Change in x: 7 - 1 = 6

Slope: -6/6 = -1

Equation of the perpendicular bisector:

The slope, multiplied with the slope of segment AB, is -1. So

$-1m = -1$

$m = 1$

So

$y = x + b$

Passes through (4,2), which means that when $x = 4, y = 2$. So

$y = x + b$

$2 = 4 + b$

$b = -2$

So

$y = x - 2$