Answer :
Answer:
p = -4, q = -3
Step-by-step explanation:
y = -2x +4 ... (1) perpendicular bisector of AB, slope = -2
slope of AB = 1/2
Line AB pass (8,3): (y-3) / (x-8) = 1/2
AB equation: y-3 = 1/2(x-8) y = 1/2x - 1 ... (2)
(2)-(1): 5/2 x = 5 x = 2
y = 0 (2,0) intercept of bisector and AB, it is midpoint of A (8,3) and (p,q)
(8+p)/2 = 2
p = -4
(3+q)/2 = 0
q = -3
The values of p and q from the perpendicular bisector are;
p = -4 and q = -3
We are given coordinates of A and B as;
A(8, 3) and B(p, q)
Bisector of AB is y = -2x + 4
Thus, from y = mx + c, Slope of the bisector is -2.
Since the bisector is perpendicular to AB, then slope of AB = -(1/-2) = 1/2
Thus, slope of the line from point A to the point of the bisector on AB is;
(y - 3)/(x - 8) = 1/2
y - 3 = ¹/₂(x - 8)
y - 3 = ¹/₂x - 4
y = ¹/₂x - 1
Putting ¹/₂x - 1 for y in the bisector equation gives;
¹/₂x - 1 = -2x + 4
2x + ¹/₂x = 4 + 1
2.5x = 5
x = 5/2.5
x = 2
Thus;
y = -2(2) + 4
y = 0
Thus, the coordinate of the midpoint of AB is (2, 0)
Now, this means that;
(8 + p)/2 = 2
8 + p = 4
p = 4 - 8
p = 4
Also; (3 + q)/2 = 0
3 + q = 0
q = -3
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