Question

lesson 4 homework
date
period
quadrilateral hdwm is shown on the coordinate grid.
draw the quadrilateral that is the result of a translation right 8 units and up 3 units
and then reflected across the y - axis. label the new quadrilateral ybkt.
complete the table.
2.
3.

1. complete the table of values for each quadrilateral.
2. explain how the tables for quadrilaterals hdwm and hdwm show the effect of

the transformation on the coordinates that result in the algebraic description.

1. explain how the tables for quadrilaterals hdwm and ybkt show the effect of the

transformation on the coordinates that result in the algebraic description.

Explanation:

Step1: Analyze the translation

For the translation \(HDWM
ightarrow H'D'W'M'\), we know that if a point \((x,y)\) is translated right \(8\) units (add \(8\) to the \(x -\) coordinate) and up \(3\) units (add \(3\) to the \(y -\) coordinate). For example, for point \(H(-7,4)\):
\(x=-7 + 8=1\), \(y = 4+3 = 7\), so \(H'(1,7)\). In general, the algebraic rule is \((x,y)\to(x + 8,y+3)\)

Step2: Analyze the reflection

For the reflection \(H'D'W'M'\to YBKT\) across the \(y -\) axis. The rule for a reflection across the \(y -\) axis is \((x,y)\to(-x,y)\). For example, if we have a point \(H'(1,7)\), then after reflection \(x=-1,y = 7\) (point \(Y(-1,7)\))

Step3: Explain the translation effect on coordinates (Question 5)

Looking at the table for \(HDWM\) and \(H'D'W'M'\):

• For the \(x -\) coordinates:

Take \(H(-7,4)\) and \(H'(1,7)\). \(-7+8 = 1\), \(D(-9,1)\) and \(D'(4,9)\) \(-9 + 8=4\) (wait, correction: \(-9+8=-1\) (error in previous hand - written, but based on the rule \((x,y)\to(x + 8,y + 3)\)). In general, for each vertex \((x,y)\) of \(HDWM\), the \(x -\) coordinate of the corresponding vertex of \(H'D'W'M'\) is \(x+8\) and the \(y -\) coordinate is \(y + 3\)

Step4: Explain the reflection effect on coordinates (Question 6)

Looking at the table for \(H'D'W'M'\) and \(YBKT\):
Take \(H'(1,7)\) and \(Y(-1,7)\), \(D'(4,4)\) and \(B(-4,4)\). For each vertex \((x,y)\) of \(H'D'W'M'\), the \(x -\) coordinate of the corresponding vertex of \(YBKT\) is \(-x\) and the \(y -\) coordinate remains \(y\) (since reflection across the \(y -\) axis changes the sign of the \(x -\) coordinate while keeping the \(y -\) coordinate the same)

Answer:

1. For each vertex \((x,y)\) of \(HDWM\), the \(x -\) coordinate of the corresponding vertex of \(H'D'W'M'\) is obtained by \(x+8\) (right - translation by \(8\) units) and the \(y -\) coordinate is obtained by \(y + 3\) (up - translation by \(3\) units)
2. For each vertex \((x,y)\) of \(H'D'W'M'\), the \(x -\) coordinate of the corresponding vertex of \(YBKT\) is \(-x\) (reflection across the \(y -\) axis changes the sign of the \(x -\) coordinate) and the \(y -\) coordinate remains \(y\)