Question

Madelyn incorrectly followed the set of directions when she transformed pentagon PENTA.The directions are listed below the coordinate plane. What was the error Madelyn made?A. She rotated, but not 180°B. She reflected over the x-axis instead of the y-axisC. She translated 4 units to the left instead of the rightD. She did not make a mistake

Answer 1

Given the transformation below:

Given the directions:

`\begin{gathered} Rotate\text{ 180 degrees} \\ Reflect\text{ over the y-axis} \\ Translate\text{ 4 unnts to the right} \end{gathered}`

Step 1: Give the coordinates of the vertices of pentagon PENTA.

Thus,

`\begin{gathered} P(-5,5) \\ E(-3,\text{ 5\rparen} \\ N(-4,\text{ 4\rparen} \\ T(-3,\text{ 2\rparen} \\ A(-5,\text{ 2\rparen} \end{gathered}`

step 2: Rotate the pentagon 180 degrees.

For 180 degrees rotation, we have

`\begin{gathered} A(x,y)\to A^(\prime)(-x,\text{ -y\rparen} \\ where \\ A^(\prime)\text{ is an image of A} \end{gathered}`

Thus, the coordinates of pentagon becomes

`\begin{gathered} P(5,\text{ -5\rparen} \\ E(3,\text{ -5\rparen} \\ N(4,\text{ -4\rparen} \\ T(3,\text{ -2\rparen} \\ A(5,\text{ -2\rparen} \end{gathered}`

The image is shown below:

step 3: Reflect over the y-axis.

For reflection over the y-axis, we have

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

This, we have the image to be

step 4: Translate 4 units to the right.

For translation by 4 units to the right, we have

`(x,y)\to(x+4,\text{ y\rparen}`

This gives

Hence, the mistake Madelyn made was that she reflected over the x-axis instead of the y-axis.

The correct option is B.