First slide

Cartesian plane

Question

At what point the origin be shifted, if the, coordinates of a point (4, 5) become (-3, 9)?

Moderate

A

$(- 7, 4)$
B

$(7, - 4)$
C

$(1, 14)$
D

$(- 4, 7)$

Solution

Let (h,k) be the point to which the origin is shifted. Then,
$\begin{aligned} x = 4, y = 5, X = - 3, Y = 9 \end{aligned}$
$∴ x = X + h$ and $y = γ + k$
$\Rightarrow 4 = - 3 + h$ and $5 = 9 + k \Rightarrow h = 7$ and $k = - 4$
Hence, the origin must be shifted to (7, - 4)

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