Final answer:
To determine the equation of the perpendicular bisector of segment QR with coordinates Q(-3,4) and R(7, 0), we first find the midpoint of the segment, then calculate the slope of the perpendicular bisector using the negative reciprocal of the slope of QR. Finally, we use the point-slope form of a line to find the equation.
Step-by-step explanation:
To determine the equation of the perpendicular bisector of segment QR, we first find the midpoint of segment QR, which is the point M. The coordinates of M can be found by taking the average of the x-coordinates and the average of the y-coordinates of Q and R:
M = ((-3 + 7)/2, (4 + 0)/2) = (2, 2)
The slope of segment QR can be found using the formula:
slope QR = (y2 - y1)/(x2 - x1) = (0 - 4)/(7 - (-3)) = -4/10 = -2/5
The slope of the perpendicular bisector is the negative reciprocal of the slope of QR. The negative reciprocal of -2/5 is 5/2. Now we use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
y - 2 = 5/2(x - 2)
y - 2 = 5/2x - 5
y = 5/2x - 3