Question

date period lesson 4 homework quadrilateral hdwm is shown on the coordinate grid. 1. 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.

Explanation:

Step1: Find the coordinates of the original quadrilateral HDWM

Assume the coordinates of \(H\), \(D\), \(W\), \(M\) are \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\), \((x_4,y_4)\) respectively.

Step2: Apply the reflection across the \(y\) - axis

The rule for reflection across the \(y\) - axis is \((x,y)\to(-x,y)\). So the new coordinates of the reflected points \(H'\), \(D'\), \(W'\), \(M'\) are \((-x_1,y_1)\), \((-x_2,y_2)\), \((-x_3,y_3)\), \((-x_4,y_4)\) respectively.

Step3: Apply the translation

The rule for translation \(8\) units right and \(3\) units up is \((x,y)\to(x + 8,y+3)\). So the final coordinates of the points \(Y\), \(B\), \(K\), \(T\) (corresponding to the translated - reflected points) are \((-x_1+8,y_1 + 3)\), \((-x_2+8,y_2+3)\), \((-x_3+8,y_3+3)\), \((-x_4+8,y_4+3)\) respectively. Then plot these points on the coordinate grid to form the quadrilateral \(YBKT\).

Since the original coordinates of \(H(- 4,-7)\), \(D(-1,-4)\), \(W(2,-6)\), \(M(0,-9)\)

• For reflection across \(y\) - axis: \(H'=(4,-7)\), \(D'=(1,-4)\), \(W'=(-2,-6)\), \(M'=(0,-9)\)
• For translation \(8\) units right and \(3\) units up:
• \(Y=(4 + 8,-7+3)=(12,-4)\)
• \(B=(1 + 8,-4 + 3)=(9,-1)\)
• \(K=(-2+8,-6 + 3)=(6,-3)\)
• \(T=(0 + 8,-9+3)=(8,-6)\)

Answer:

Plot the points \(Y(12,-4)\), \(B(9,-1)\), \(K(6,-3)\), \(T(8,-6)\) on the coordinate grid and connect them to form the quadrilateral \(YBKT\).