Question

6.) here are the pre - image and image coordinates of a figure. no grid has been provided. describe a possible transformation that took place for each set of pre - image and images.

pre - image coordinate	image coordinates	possible transformation
(-3, 5)	(-3, -5)
(6, -4)	(6, 4)

Explanation:

To determine the transformation, we analyze each pair of pre - image and image coordinates:

For the pair \((-2,1)\) and \((-2, - 1)\)

• The \(x\) - coordinate remains the same (\(-2=-2\)), and the \(y\) - coordinate changes from \(1\) to \(-1\). We can see that \(1\times(- 1)=-1\).

For the pair \((-3,5)\) and \((-3,-5)\)

• The \(x\) - coordinate remains the same (\(-3 = - 3\)), and the \(y\) - coordinate changes from \(5\) to \(-5\). We can see that \(5\times(-1)=-5\).

For the pair \((6,-4)\) and \((6,4)\)

• The \(x\) - coordinate remains the same (\(6 = 6\)), and the \(y\) - coordinate changes from \(-4\) to \(4\). We can see that \(-4\times(-1)=4\).

In general, if we have a pre - image point \((x,y)\) and the image point is \((x,-y)\), this represents a reflection over the \(x\) - axis. The rule for a reflection over the \(x\) - axis is \((x,y)\to(x, - y)\).

For the first row (pre - image \((-2,1)\), image \((-2,-1)\))

Using the reflection over \(x\) - axis rule: When \(x=-2\) and \(y = 1\), the image should be \((-2,-1)\), which matches.

For the second row (pre - image \((-3,5)\), image \((-3,-5)\))

Using the reflection over \(x\) - axis rule: When \(x=-3\) and \(y = 5\), the image should be \((-3,-5)\), which matches.

For the third row (pre - image \((6,-4)\), image \((6,4)\))

Using the reflection over \(x\) - axis rule: When \(x = 6\) and \(y=-4\), the image should be \((6,4)\) (since \(-y=-(-4) = 4\)), which matches.

So the possible transformation for each set of pre - image and image coordinates is a reflection over the \(x\) - axis.

For the first set (pre - image \((-2,1)\), image \((-2,-1)\)): Reflection over \(x\) - axis.

For the second set (pre - image \((-3,5)\), image \((-3,-5)\)): Reflection over \(x\) - axis.

For the third set (pre - image \((6,-4)\), image \((6,4)\)): Reflection over \(x\) - axis.

Answer:

To determine the transformation, we analyze each pair of pre - image and image coordinates:

For the pair \((-2,1)\) and \((-2, - 1)\)

• The \(x\) - coordinate remains the same (\(-2=-2\)), and the \(y\) - coordinate changes from \(1\) to \(-1\). We can see that \(1\times(- 1)=-1\).

For the pair \((-3,5)\) and \((-3,-5)\)

• The \(x\) - coordinate remains the same (\(-3 = - 3\)), and the \(y\) - coordinate changes from \(5\) to \(-5\). We can see that \(5\times(-1)=-5\).

For the pair \((6,-4)\) and \((6,4)\)

• The \(x\) - coordinate remains the same (\(6 = 6\)), and the \(y\) - coordinate changes from \(-4\) to \(4\). We can see that \(-4\times(-1)=4\).

In general, if we have a pre - image point \((x,y)\) and the image point is \((x,-y)\), this represents a reflection over the \(x\) - axis. The rule for a reflection over the \(x\) - axis is \((x,y)\to(x, - y)\).

For the first row (pre - image \((-2,1)\), image \((-2,-1)\))

Using the reflection over \(x\) - axis rule: When \(x=-2\) and \(y = 1\), the image should be \((-2,-1)\), which matches.

For the second row (pre - image \((-3,5)\), image \((-3,-5)\))

Using the reflection over \(x\) - axis rule: When \(x=-3\) and \(y = 5\), the image should be \((-3,-5)\), which matches.

For the third row (pre - image \((6,-4)\), image \((6,4)\))

Using the reflection over \(x\) - axis rule: When \(x = 6\) and \(y=-4\), the image should be \((6,4)\) (since \(-y=-(-4) = 4\)), which matches.

So the possible transformation for each set of pre - image and image coordinates is a reflection over the \(x\) - axis.

For the first set (pre - image \((-2,1)\), image \((-2,-1)\)): Reflection over \(x\) - axis.

For the second set (pre - image \((-3,5)\), image \((-3,-5)\)): Reflection over \(x\) - axis.

For the third set (pre - image \((6,-4)\), image \((6,4)\)): Reflection over \(x\) - axis.