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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

Madelyn Incorrectly Followed The Set Of Directions When She Transformed Pentagon PENTAThe Directions Are Listed Below The Coordinate Plane What Was The Error M class=

Sagot :

Solution:

Given the transformation below:

Given the directions:

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

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

Thus,

[tex]\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}[/tex]

step 2: Rotate the pentagon 180 degrees.

For 180 degrees rotation, we have

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

Thus, the coordinates of pentagon becomes

[tex]\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}[/tex]

The image is shown below:

step 3: Reflect over the y-axis.

For reflection over the y-axis, we have

[tex](x,y)\to(-x,y)[/tex]

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

[tex](x,y)\to(x+4,\text{ y\rparen}[/tex]

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.

View image ElisiaY275369
View image ElisiaY275369
View image ElisiaY275369
View image ElisiaY275369
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