The point P has coordinates (1,10) and the point Q has coordinates (4,4).
(a) Show the length of PQ is 3 squared 5.
(b) (i) Find the equation of the perpendicular bisector of PQ.
(ii) This perpendicular bisector intersects the x-axis at the point A. Find the coordinates of A.
to (a): Use the distance formula
to (b)(i)
1. Calculate the slope
2. Calculate the perpendicular direction to this slope
3. Calculate the coordinates of the mid point of PQ:
4. Use the point-slope-formula to get the equation of the perpendicular bisector.
to (b)(ii)
Solve the equation y = 0 using the equation of (b)(i)4
Find the midpoint of PQ.
Find the slop of PQ.
The slope of the perpendicular will be the negative reciprocal of that slope which is
The equation of the perpendicular will have slope = 1/2 and pass through the midpoint of PQ which is (5/2, 7).
y = mx + b
The above is the equation of the perpendicular in slope-intercept form.
General form would be
To find the x-intercept, simply assign 0 to y and solve for x. The coordinates will be in the form (x, 0).