Given that the perpendicular bisector of the line joining A(4,3) and B is 5y=x-2, find the coordinates of B.

Answer 1

The equation of the line passing through A and B is y - 3 = -5(x-4) or y = -5x + 23. This is because the slope of the perpendicular bisector is 1/5 (solve 5y=x-2) for y. That equation can be written as y = (1/5)x - (2/5).

Solve for the point of intersection of the two lines (using substitution).

-5x+23 = (1/5)x-(2/5)

-25x+115=x-2 (multiply every term by 5 to clear fractions)

117 = 26x

x=4.5

y = -5(4.5)+23 = .5

So the point of intersection is (4.5. 0.5). And the whole point is that this is also the midpoint of segment AB.

Let (x₁,y₁) be the coordinates of B.

Then using the midpoint formula we have (remembering that the coordinates of A are (4,3)):

:(4+x₁)/2 = 4.5

x₁=5

(3+y₁)/2 = 1/2

y₁=-2

The coordinates of B are (5,-2).

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