If the origin is shifted to the point 0′(2, 3), the axes remaining p

1.	If the origin is shifted to the point 0′(2, 3), the axes remaining parallel to the original axes, find the new co-ordinates of the points i. A(1, 3) ii. B(2,5)
Answer» Origin is shifted to (2, 3) = (h, k) Let the new co-ordinates be (X, Y). x = X + handy = Y + k x = X + 2 and y = Y + 3 …(i) i. Given, A(x, y) = A( 1, 3) x = X + 2 andy = Y + 3 …[From(i)] ∴ 1 = X + 2 and 3 = Y + 3 X = – 1 and Y = 0 ∴ The new co-ordinates of point A are (- 1,0). ii. Given, B(x, y) = B(2, 5) x = X + 2 and y = Y + 3 …[From(i)] ∴ 2 = X + 2 and 5 = Y + 3 ∴ X = 0 and Y = 2 ∴ The new co-ordinates of point B are (0, 2).

If the origin is shifted to the point 0′(2, 3), the axes remaining parallel to the original axes, find the new co-ordinates of the points i. A(1, 3) ii. B(2,5)

Answer»

Origin is shifted to (2, 3) = (h, k)

Let the new co-ordinates be (X, Y).

x = X + handy = Y + k

x = X + 2 and y = Y + 3 …(i)

i. Given, A(x, y) = A( 1, 3)

x = X + 2 andy = Y + 3 …[From(i)]

∴ 1 = X + 2 and 3 = Y + 3 X = – 1 and Y = 0

∴ The new co-ordinates of point A are (- 1,0).

ii. Given, B(x, y) = B(2, 5)

x = X + 2 and y = Y + 3 …[From(i)]

∴ 2 = X + 2 and 5 = Y + 3

∴ X = 0 and Y = 2

∴ The new co-ordinates of point B are (0, 2).

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If the origin is shifted to the point 0′(2, 3), the axes remaining parallel to the original axes, find the new co-ordinates of the points i. A(1, 3) ii. B(2,5)

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