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Question
If the co-ordinates A(5, 14) change to B(8, 3) by shift of origin, find the co-ordinates of the point where the origin is shifted
Solution
Let (X, Y) be the new coordinates of (x, y) when the origin is shifted to the point (h, k), axes remaining parallel.
Then by the formulae for the shift of origin,
x = X + h and y = Y + k
Here x = 5, X = 8, y = 14, Y = 3
∴ 5 = 8 + h and 14 = 3 + k
∴ h = – 3 and k = 11
∴ the coordinates of the new origin are (–3, 11).
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