Question

Graph 1(90°,0)(FGHJ).Which graph below shows the preimage FGHJ and the image F'G'H''?

Answer 1

Given the figure FGHJ with coordinates

F(0, 5), G(-5, 1), H(5, -7) and J(6, 4)

When we rotate a figure of 90 degrees clockwise, each point of the given figure has to be changed from (x, y) to (y, -x) and graph the rotated figure.

Therefore, for clockwise rotation, the coordinates of the image of FGHJ becomes

`\begin{gathered} \text{ F(0, 5)}\to\text{ F'(5, 0)} \\ \text{ G(-5,}1)\to\text{ G'(1, 5)} \\ \text{ H(5, -7)}\to\text{ H'(-7, -5)} \\ \text{ J(6, 4)}\to\text{ J'(4, -6)} \end{gathered}`

Note that, the blue graph represents the pre-image FGHJ and the green graph represents the image F'G'H'J'

When we rotate a figure of 90 degrees anti-clockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure.

Therefore, the anti-clockwise rotation the coordinates of the image of FGHJ becomes

`\begin{gathered} \text{ F(0, 5)}\to\text{ F'(-5, 0)} \\ \text{ G(-5,}1)\to\text{ G'(-1, -5)} \\ \text{ H(5, -7)}\to\text{ H'(7, 5)} \\ \text{ J(6, 4)}\to\text{ J'(-4, 6)} \end{gathered}`

Note that, the blue graph represents the pre-image FGHJ and the green graph represents the image F'G'H'J'