Question

Triangle ABC has vertices A(4, -5), B(8, 11) and C(0, 15).What is the equation of the perpendicular bisector of side AC?Use point-slope form for your final equation.

Answer 1

The equation of the perpendicular bisector of side AC is y = (1/5)x + 3.

Step-by-step explanation:

To find the equation of the perpendicular bisector of side AC, we first need to find the midpoint of side AC. The midpoint is the average of the x-coordinates and the average of the y-coordinates of the endpoints. For AC, the midpoint is (2, 5).

The slope of AC can be found using the formula: slope = (y2 - y1) / (x2 - x1). For AC, the slope is (15 - (-5)) / (0 - 4) = 20 / -4 = -5.

The slope of a perpendicular line is the negative reciprocal of the slope of the original line. So, the slope of the perpendicular bisector of AC is 1/5. Using the point-slope form, the equation of the perpendicular bisector is y - 5 = (1/5)(x - 2), which simplifies to y = (1/5)x + 3.