Chapter 12, Problem 3CR

To determine

To find : the coordinates of P’ when the figure of $P\left(x,y\right)$ reflected to the $x$ -axis and rotated ${180}^{\circ }$ and dilated using a scale factor of $2$ .

Answer to Problem 3CR

The coordinates of P’ when the figure of $P\left(x,y\right)$ reflected to the $x$ -axis is $P\text{'}\left(x,-y\right)$ .

The coordinates of P’ when the figure of $P\left(x,y\right)$ rotated ${180}^{\circ }$ is $P\text{'}\left(-x,-y\right)$ .

The coordinates of P’ when the figure of $P\left(x,y\right)$ dilated using a scale factor of $2$ is $P\text{'}\left(2x,2y\right)$ .

Explanation of Solution

Given : the pointprovided in the question,

  $P\left(x,y\right)$

Calculation: when the figure reflected in the $x$ -axis, the y -coordinate of the reflected figure multiply by -1.

  $P\left(x,y\right)\to P\text{'}\left(x,-y\right)$

When the figure rotated ${180}^{\circ }$ , the coordinates of the figure multiply by -1.

  $P\left(x,y\right)\to P\text{'}\left(-x,-y\right)$

When the figure dilated using a scale factor of 2, the coordinates multiply by 2.

  $P\left(x,y\right)\to P\text{'}\left(2x,2y\right)$

Hence,

The coordinates of P’ when the figure of $P\left(x,y\right)$ reflected to the $x$ -axis is $P\text{'}\left(x,-y\right)$ .

The coordinates of P’ when the figure of $P\left(x,y\right)$ rotated ${180}^{\circ }$ is $P\text{'}\left(-x,-y\right)$ .

The coordinates of P’ when the figure of $P\left(x,y\right)$ dilated using a scale factor of $2$ is $P\text{'}\left(2x,2y\right)$ .