Question

Triangle abc has the following points: a (-2,-2), b(4,4), c(18,-6). Use these points to write the equations of the line containing the perpendicular bisector of segment of line ac in point form.

Answer 1

To write the equation of the line containing the perpendicular bisector of segment AC, find the midpoint of AC and determine the slope of the perpendicular bisector. The equation of the line is y = (5/2)x - 24.

Step-by-step explanation:

To write the equation of the line containing the perpendicular bisector of segment AC, we need to find the midpoint of AC and determine the slope of the perpendicular bisector. The midpoint of AC can be found by averaging the x-coordinates and the y-coordinates of A and C:

Midpoint = ((-2 + 18) / 2, (-2 + -6) / 2) = (8, -4)

The slope of the line AC is given by:

Slope = (y2 - y1) / (x2 - x1) = (-6 - (-2)) / (18 - (-2)) = -8/20 = -2/5

The slope of the perpendicular bisector is the negative reciprocal of the slope of AC, which is 5/2. Now we can write the equation of the line in point-slope form using the midpoint (8, -4):

y - y1 = m(x - x1)

y - (-4) = (5/2)(x - 8)

y + 4 = (5/2)(x - 8)

y + 4 = (5/2)x - 20

y = (5/2)x - 24

Therefore, the equation of the line containing the perpendicular bisector of segment AC in point form is y = (5/2)x - 24.