Final answer:
To find the equation of the perpendicular bisector of side BC, first find the midpoint of BC, calculate the slope of BC, find the negative reciprocal of the slope to get the slope of the perpendicular bisector, and then use the formula for the equation of a line to find the equation.
Step-by-step explanation:
To find the equation of the perpendicular bisector of side BC, we first need to find the midpoint of BC. The midpoint can be found by averaging the x-coordinates and the y-coordinates of B and C. So, the midpoint is M(((-5+5)/2),((-6+0)/2)) = M(0,-3).
Next, we find the slope of side BC using the formula: slope = (y2 - y1) / (x2 - x1). The slope of BC is (-6 - 0) / (-5 - 5) = -6 / -10 = 3/5.
Since the line we are looking for is perpendicular to BC, the slope of the perpendicular bisector is the negative reciprocal of the slope of BC. So, the perpendicular bisector has a slope of -5/3.
Lastly, we use the formula for the equation of a line y = mx + b to find the equation. Plugging in the midpoint (0,-3) and the slope -5/3, we have y = -5/3x - 3 as the equation of the perpendicular bisector of side BC.