P (5,) and Q (-1, 2) are points on a straight line. Find the equation of the perpendicular bisector of PQ: y = mx+c
Perpendicular bisector is the negative reciprocal of the slope so if the slope is 2 the negative reciprocal is -1/2.
how do you get?
what is the coordinates of P
To find the equation of the perpendicular bisector of PQ, we need to find the slope (m) and the y-intercept (c).
Step 1: Find the midpoint of line PQ.
The midpoint of a line segment is the average of the coordinates of its endpoints. Let's find the x-coordinate and y-coordinate of the midpoint (M).
x-coordinate of M = (x1 + x2) / 2 = (5 + (-1)) / 2 = 4 / 2 = 2
y-coordinate of M = (y1 + y2) / 2 = (0 + 2) / 2 = 2 / 2 = 1
So, the midpoint M of line PQ is (2, 1).
Step 2: Find the slope of line PQ.
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: m = (y2 - y1) / (x2 - x1).
Using points P(5, 0) and Q(-1, 2):
m = (2 - 0) / (-1 - 5) = 2 / -6 = -1/3
Step 3: Find the negative reciprocal of the slope to get the perpendicular slope.
The negative reciprocal of -1/3 is 3.
Step 4: Substitute the midpoint coordinates and the perpendicular slope into the equation y = mx + c and solve for c.
Using the coordinates of the midpoint M(2, 1) and the perpendicular slope of 3:
1 = 3 * 2 + c
1 = 6 + c
c = 1 - 6
c = -5
So, the equation of the perpendicular bisector of PQ is y = 3x - 5.