Find an equation of the line described. Leave the solution in the form Ax + By = C. The line is the perpendicular bisector of the line segment that joins (2, 7) and (6, −1).

Question

Find an equation of the line described. Leave the solution in the form Ax + By = C.

The line is the perpendicular bisector of the line segment that joins (2, 7) and (6, −1).

Answer 1

perpendicular bisector means a line that runs through another at the midpoint (halfway) forming a right angle.

perpendicular lines have opposite reciprocal slopes.

1. Find the midpoint between the two points given by finding the average of the x coordinates and the average of the y coordinates.

M= (2+6/2. , 7+ -1/2) =( 4, 3 )

This gives us a point that the unknown line goes

through

2. Find the slope of the unknown line by finding the slope

of the given points and then taking its opposite

reciprocal by taking difference of y coordinates over the

difference of the x coordinates

m = (7- -1) / (2-6) = 8/-4 = -2

opposite reciprocal = 1/2

3.use the midpoint and the opposite reciprocal slope to

write the equation in point slope or slope intercept form.

Then rearrange to standard form.

Point/slope= y-y1= m(x-x1). Y-3 =1/2(x-4)

Rearrange to slope intercept . Y= 1/2X+1

Rearrange to standard -1/2x+y=1

Standard cannot have fractions nor negative A

Multiply all terms by -2. X-2y=-2

Slope/intercept y=mx+b. 3=1/2(4)+b.

Solve for b. 3=2+b. 1=b. Y=1/2x+1

Rearrange to standard -1/2x+y=1

Standard cannot have fractions nor negative A

Multiply all terms by -2. X-2y=-2

Answer 2

(2,7), (6,-1) averaged give the midpoint (4,3)

a line through (2,7) and (6,-1) has slope = (7--1)/(2-6) = 8/-4 = -2

a perpendicular line has a negative inverse slope, take -2 change its sign and flip it upside down to get 1/2

y=(-1/2)x + b, solve for b by plugging in the point (4,3)

3 =-4/2+b

b = 3+2 = 5

y=-x/2 +5 or

2y=-x +10

x+2y = 10, in the form Ax +By = C with A=1, B=2, C=10