Find an equation for the perpendicular bisector of the line segment whose endpoints are (1,6) and (-9,-2)

Answer 1

We need to find the midpoint and the slope.

The midpoint is ((1+(-9))/2,(6+(-2))/2) = (-8)/2,4/2) = (-4,2)

The slope is [6-(-2]/[1-(-9)] = 8/10 = 4/5

The perpendicular slope is the negative reciprocal which is -5/4

2 = (-5/4)(-4) + b

2 = 5 + b

b = -3

y = (-5/4)x - 3

Answer 2

Step 1: Find the slope of the line between (1, 6) and (-9, 2).

To do that, use the slope equation:

m = (y₂ - y₁)/(x₂ - x₁) where "m" is the slope, x₁ is the x-coordinate of the first point, x₂ is the x-coordinate of the second point, y₁ is the y-coordinate of the first point, and y₂ is the y-coordinate of the second point.

m = (-2 - 6)/(-9 - 1) = -8/-10 = 8/10 = 4/5

Step 2, Convert the slope found in Step 1 to the slope of the perpendicular.

To do that, take the negative reciprocal (flip the fraction over and put a negative sign in front). So the slope of the perpendicular is -5/4

Step 3. Find the midpoint (the point in the middle of the segment).

To do this, add the two x-values together and divide by 2 so the x-value of the midpoint is (1 + -9)/2 = -4

To find the y-value of the midpoint, add the two y-values and divide by 2 so the y-value of the midpoint is (6 + -2)/2 = 2

So the midpoint is (-4, 2)

Step 4. Use the point-slope form of a line to get the equation

To do that use the point you got from step 3 and the slope you got from step 2. The point-slope form is:

y - y₁ = m(x - x₁) where (x₁, y₁) is the point and "m" is the slope. Note: This x₁ and y₁ are not related to the x₁ and y₁ you used in step 1. Here you use x₁ = -4 and y₁ = 2 (from Step 3) so:

y - y₁ = m(x - x₁)

y - 2 = -5/4(x - -4)

y - 2 = -5/4(x + 4)

y - 2 = (-5/4)x - 5

y = (-5/4)x - 3