Question

geometry unit 4 lesson 2 homework five quadrilaterals are shown on the coordinate grid. 1. draw the reflection of quadrilateral mptz across the line y = x. label the reflection as mptz. 2. draw the reflection of quadrilateral vkgq across the line y = -x. label the reflection as vkgq. 3. select all of the quadrilaterals that are reflections of quadrilateral ybrn. quadrilateral whcx quadrilateral mptz quadrilateral kvqg quadrilateral sfdl quadrilateral mptz quadrilateral kvqg 4. the algebraic description of the reflection of quadrilateral bynr, the preimage, onto quadrilateral pmzt, the image, is (x,y)→(-x,y). describe how the coordinates of the vertices of quadrilateral bynr, the preimage, and the coordinates of quadrilateral pmzt, the image, can be used to determine the line of reflection.

Explanation:

Step1: Recall reflection rules

For reflection across $y = x$, the transformation is $(x,y)\to(y,x)$. For reflection across $y=-x$, the transformation is $(x,y)\to(-y,-x)$. To check if two quadrilaterals are reflections of each other, we can compare vertex - to - vertex distances and orientations. For a reflection of the form $(x,y)\to(-x,y)$, the line of reflection is the y - axis.

Step2: Answer question 1

To reflect quadrilateral $MPTZ$ across $y = x$, for each vertex $(x,y)$ of $MPTZ$, we swap the $x$ and $y$ coordinates to get the vertices of $M'P'T'Z'$.

Step3: Answer question 2

To reflect quadrilateral $VKGQ$ across $y=-x$, for each vertex $(x,y)$ of $VKGQ$, we change it to $(-y,-x)$ to get the vertices of $V'K'G'Q'$.

Step4: Answer question 3

By visually inspecting the orientation and vertex - to - vertex distances of the quadrilaterals on the coordinate grid, we find that quadrilaterals $WHCX$ and $MPTZ$ are reflections of $YBRN$.

Step5: Answer question 4

If the algebraic description of the reflection is $(x,y)\to(-x,y)$, we note that the $y$ - coordinate remains the same and the $x$ - coordinate changes sign. This means that the line of reflection is the vertical line $x = 0$, which is the y - axis.

Answer:

1. Follow the rule $(x,y)\to(y,x)$ for each vertex of $MPTZ$ to draw $M'P'T'Z'$.
2. Follow the rule $(x,y)\to(-y,-x)$ for each vertex of $VKGQ$ to draw $V'K'G'Q'$.
3. A. Quadrilateral $WHCX$, B. Quadrilateral $MPTZ$
4. The line of reflection is the y - axis. The $y$ - coordinates of corresponding vertices in the pre - image ($BYNR$) and the image ($PMZT$) are equal, and the $x$ - coordinates of corresponding vertices have opposite signs. So the line of reflection is $x = 0$.