# CBSE 2017 Board Solution

Class 10 Math - AI Set 3 - Q8. Coordinate Geometry

#### Video Explanation

Distance between two points whose coordinates are (x1, y1) and (x2, y2) = $$sqrt {{${{x}_{2}}-{{x}_{1}}$}^{2}+{({{y}_{2}}-{{y}_{1}})}^{2}})

##### Given information

Distance between P(x, y) and A(5, 1) = distance between P(x, y) and B(-1, 5)
Distance between P and A = $$sqrt {{$x-5$}^{2}+{(y-1)}^{2}})
Distance between P and B = $$sqrt {{$x+1$}^{2}+{(y-5)}^{2}})

Equate the two distances and solve for x and y.
$$sqrt {{$x-5$}^{2}+{(y-1)}^{2}}) = $$sqrt {{$x+1$}^{2}+{(y-5)}^{2}})

Square both the sides of the equation
(x – 5)2 + (y - 1)2 = (x + 1)2 + (y – 5)2
x2 – 10x + 25 + y2 – 2y + 1 = x2 + 2x + 1 + y2 – 10y + 25
-12x = -8y
Or 12x = 8y
Or 3x = 2y

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