Question

determine the coordinates of each point after the shaded pre-image is reflected over the x-axis. use the graph if it helps with your thinking. pre-image coordinates image coordinates (-2, 0) (-2, 2) (-1, 3) (1, 3) (0, 1)

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is that the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. So, if the pre - image point is \((x,y)\), the image point after reflection over the \(x\) - axis is \((x, - y)\).

Step2: Reflect \((-2,0)\)

For the point \((-2,0)\), using the rule \((x,y)\to(x, - y)\), we substitute \(x=-2\) and \(y = 0\). Then \(-y=-0 = 0\). So the image coordinate is \((-2,0)\).

Step3: Reflect \((-2,2)\)

For the point \((-2,2)\), using the rule \((x,y)\to(x, - y)\), we substitute \(x = - 2\) and \(y=2\). Then \(-y=-2\). So the image coordinate is \((-2,-2)\).

Step4: Reflect \((-1,3)\)

For the point \((-1,3)\), using the rule \((x,y)\to(x, - y)\), we substitute \(x=-1\) and \(y = 3\). Then \(-y=-3\). So the image coordinate is \((-1,-3)\).

Step5: Reflect \((1,3)\)

For the point \((1,3)\), using the rule \((x,y)\to(x, - y)\), we substitute \(x = 1\) and \(y=3\). Then \(-y=-3\). So the image coordinate is \((1,-3)\).

Step6: Reflect \((0,1)\)

For the point \((0,1)\), using the rule \((x,y)\to(x, - y)\), we substitute \(x = 0\) and \(y=1\). Then \(-y=-1\). So the image coordinate is \((0,-1)\).

Answer:

Pre - Image Coordinates	Image Coordinates
\((-2,2)\)	\((-2,-2)\)
\((-1,3)\)	\((-1,-3)\)
\((1,3)\)	\((1,-3)\)
\((0,1)\)	\((0,-1)\)