Question

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. 2. complete the table. transformation mapping hdwm→ybkt algebraic description

Explanation:

Step1: Apply translation rule

For a translation right 8 units and up 3 units, the rule for a point $(x,y)$ is $(x,y)\to(x + 8,y+3)$. Let the coordinates of the vertices of quadrilateral HDWM be $H(x_1,y_1)$, $D(x_2,y_2)$, $W(x_3,y_3)$ and $M(x_4,y_4)$. After translation, the new vertices $H'(x_1 + 8,y_1+3)$, $D'(x_2 + 8,y_2+3)$, $W'(x_3 + 8,y_3+3)$ and $M'(x_4 + 8,y_4+3)$.

Step2: Apply reflection rule

The rule for reflecting a point $(x,y)$ across the y - axis is $(x,y)\to(-x,y)$. So for the vertices $H'(x_1 + 8,y_1+3)$, $D'(x_2 + 8,y_2+3)$, $W'(x_3 + 8,y_3+3)$ and $M'(x_4 + 8,y_4+3)$ of the translated quadrilateral, after reflection across the y - axis, the vertices of quadrilateral YBKT are $Y(-(x_1 + 8),y_1+3)$, $B(-(x_2 + 8),y_2+3)$, $K(-(x_3 + 8),y_3+3)$ and $T(-(x_4 + 8),y_4+3)$.
To draw:

1. First, for each vertex of HDWM, add 8 to the x - coordinate and 3 to the y - coordinate to get the vertices of the translated quadrilateral.
2. Then, for each vertex of the translated quadrilateral, change the sign of the x - coordinate to get the vertices of YBKT. Plot these new vertices on the coordinate grid and connect them to form the quadrilateral YBKT.

For the table:

Transformation	HDWM → H'D'W'M'	H'D'W'M' → YBKT
Algebraic Description	Add 8 to x - coordinate and 3 to y - coordinate	Change the sign of the x - coordinate

Answer:

The new quadrilateral YBKT is drawn by first translating HDWM right 8 units and up 3 units and then reflecting the resulting quadrilateral across the y - axis. The mapping and algebraic descriptions for the two - step transformation are shown in the table above.