Question

If the figure below is rotated 90 degrees counter-clockwise, what is the radius of the circle that has

Answer 1

When a shape is rotated, it must be rotated through a point.

The radius of the circle is: 4

The location of point F is:

$F = (4,0)$

When the shape is rotated $90^o$ counterclockwise, the rule is:

$(x,y) \to (-y,x)$

So, the location of point F' is:

$F' = (0,4)$

The center of the circle is given as:

$O = (0,0)$

The radius of the circle is the distance from the center to point F or F'

This is calculated using the following distance formula

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

The distance from O to F is:

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

$r =\sqrt{16 + 0}$

$r =\sqrt{16}$

Take square roots

$r = \±4$

Radius cannot be negative.

So:

$r = 4$

Hence, the radius of the circle is (b) 4

Read more about rotation at:

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