Question

The unit circle has a radius of 1 unit and is centered at the origin. It is dilated so that it passes through the point (4, 0). What is the scale factor of dilation? 3 4.

Answer 1

Dilation involves changing the size of a shape (i.e. a circle)

The scale of dilation is 4

The circle passes through the origin.

So, one of the points is (0,0)

When dilated it passes through the point (4,0).

The scale factor (k) is calculated by calculating the distance between the new point and the old point.

So, we have:

$\mathbf{k = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}}$

This gives

$\mathbf{k = \sqrt{(4- 0)^2 + (0-0)^2}}$

Simplify

$\mathbf{k = \sqrt{16 +0}}$

Add 16 and 0

$\mathbf{k = \sqrt{16}}$

Take the square root of 16

$\mathbf{k =4}$

Hence, the scale of dilation is 4

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