Question

Points A and B have coordinates (8,3) and (. q) respectively. The equation of the perpendicular
bisector of AB is y-2x + 4.
Find the values of p and q.
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Answer 1

Answer:

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Answer 2

Given:

A line passes through the points (8,3) and (p,q). The equation of the line perpendicular to the given line is y - 2x + 4 = 0.

To Find:

The values of p and q.

Solution:

The given problem can be solved by using the concepts of 2D straight lines.

1. It is given that the line equation passes through (8,3) and (p,q). The equation of the line perpendicular to the original line is y - 2x +4 = 0.

2. Consider a straight line ax+by+c = 0, the equation of the line perpendicular to the given line is given as b x-ay +k = 0, where a,b are coefficients and c, k are constants.

=> The perpendicular line is - 2x + y + 4 =0, Hence the original line is,

=> Line equation = x + 2y + c =0,

3. The above line passes through the point (8,3), Therefore,

=> 8 + 6 + c = 0,

=> c = -14.

4. Therefore, the line equation is x + 2y -14 = 0.

=> p + 2q = 14. (Equation 1).

5. The equation of the straight line passing through (8,3) and (p,q) is given as,

=> Solving the given problem by using the trial and error method we get,

=> p = 4, q = 5.

Therefore, the values of p and q are 4,5 respectively.