If A(4,3) B(2,1),C(6,-1) and D(8,1) be four points, shows that AC and AD bisect eachother
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Correction: If A(4, 3) B(2, 1), C(6, -1) and D(8, 1) be four points, shows that AC and BD bisect each other
We have four points A(4, 3), B(2, 1), C(6, -1) and D(8,1).
And, we have to prove AC & BD bisect each other, i.e, we have to prove that AO = CO & BO = OD.
For any two lines to bisect each other, they must have the same midpoint.
So we'll find the midpoints of both AC & BD, compare them and see if they're the same coordinates.
Mid-point of AC:
Let the midpoint of AC be O.
x₁ ⇒ 4
x₂ ⇒ 6
y₁ ⇒ 3
y₂ ⇒ -1
Mid-point of BD:
Let the midpoint of BD be O'.
x₁ ⇒ 2
x₂ ⇒ 8
y₁ ⇒ 1
y₂ ⇒ 1
∴ O(x, y) = O'(x, y)
Hence, they bisect each other.
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