If the distances of P(x, y) from A(5, 1) and B(- 1, 5) are equal, then prove that 3x = 2y
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Answers
Given that,
The distances of P(x, y) from A(5, 1) and B(- 1, 5) are equal.
We know,
Distance Formula :- The distance between two points P(x₁, y₁) and Q(x₂, y₂) is evaluated as
Hence, Proved
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Learn More :-
1. Section formula
Let P(x₁, y₁) and Q(x₂, y₂) be two points in the coordinate plane and R(x, y) be the point which divides PQ internally in the ratio m₁ : m₂. Then, the coordinates of R will be:
2. Mid-point formula
Let P(x₁, y₁) and Q(x₂, y₂) be two points in the coordinate plane and R(x, y) be the mid-point of PQ. Then, the coordinates of R will be
3. Centroid of a triangle
Centroid of a triangle is the point where the medians of the triangle meet.
Let A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) be the vertices of a triangle. Let R(x, y) be the centroid of the triangle. Then, the coordinates of R will be:
Given,
- P = (x, y)
So A(5, 1) and B(-1, 5) can be written as (x₁, y₁) and (x₂, y₂).
It is given that PA = PB.
By Distance formula,
So applying values to the equation,
Hence Proved.