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. quadrilateral hdwm is shown on the coordinate grid.

Explanation:

Step1: Apply translation rule

The translation rule for moving right \(a\) units and up \(b\) units is \((x,y)\to(x + a,y + b)\). Here \(a = 8\) and \(b=3\). Let the coordinates of the vertices of quadrilateral \(HDWM\) be \((x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)\). After translation, the new - coordinates are \((x_1 + 8,y_1+3),(x_2 + 8,y_2 + 3),(x_3 + 8,y_3 + 3),(x_4 + 8,y_4 + 3)\).

Step2: Apply reflection rule

The reflection rule across the \(y\) - axis is \((x,y)\to(-x,y)\). After reflection across the \(y\) - axis, if the coordinates after translation are \((x',y')\), the final coordinates are \((-x',y')\).

Step3: Plot the new quadrilateral

Plot the new vertices obtained from the above - mentioned transformation steps on the coordinate grid and label the new quadrilateral \(YUKT\).

Since we don't have the actual coordinates of the vertices of quadrilateral \(HDWM\) given in text form, we can't provide numerical calculations. But the general steps for drawing are as above. When you have the coordinates of \(H\), \(D\), \(W\), and \(M\), first apply the translation \((x,y)\to(x + 8,y + 3)\) to each vertex, and then apply the reflection \((x,y)\to(-x,y)\) to the translated vertices, and finally plot the new vertices to get the quadrilateral \(YUKT\).

Answer:

Follow the steps above to draw the new quadrilateral \(YUKT\) on the coordinate - grid. First translate the vertices of \(HDWM\) right 8 units and up 3 units, then reflect the translated vertices across the \(y\) - axis and plot the new vertices.