Find the equation of the perpendicular bisector of the line joining P(2,-3) and Q(-5,1)
To find the equation of the perpendicular bisector of the line joining P(2,-3) and Q(-5,1), we first need to find the midpoint of the line segment joining P and Q, and then find the slope of the line perpendicular to the segment.
Midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Midpoint = ((2 + (-5))/2, (-3 + 1)/2)
Midpoint = (-3/2, -1)
Slope of the line joining P and Q:
m = (y2 - y1)/(x2 - x1)
m = (1 - (-3))/(-5 - 2)
m = 4/-7
m = -4/7
The slope of the line perpendicular to this line would be the negative reciprocal of -4/7, which is 7/4.
Now, we have the midpoint (-3/2, -1) and the slope 7/4, we can use the point-slope form of the equation of a line (y - y1 = m(x - x1)) to find the equation of the perpendicular bisector:
y - (-1) = 7/4(x - (-3/2))
y + 1 = 7/4(x + 3/2)
y + 1 = 7/4x + 21/8
y = 7/4x + 21/8 - 8/8
y = 7/4x + 13/8
Therefore, the equation of the perpendicular bisector of the line joining P(2,-3) and Q(-5,1) is y = 7/4x + 13/8.