Question

The new coordinates of the centre of a circle after a dilation with a scale factor of 2 are . The dilation is centered at the origin.

• A. (0,2)
• B. (2,2)
• C. (0,0)
• D. (2,0)

Answer 1

The correct option is C (0,0)


The centre of the circle is at C.

$\text{Coordinate of the point C =}(0,0)$

Let's take the new centre to be C'.

The effect of dilation can be shown as:
$C^{\prime }=(0\times 2,0\times 2)=(0,0)$

So, coordinates of point C and C' are the same.

Even after dilating the circle by a scale factor of 2, its centre will lie at the origin (0,0) only.

∴ The coordinates of the centre of the circle after dilating with scale factor 2 will be (0,0)