Question

1. quadrilateral efgh is a scale drawing of an original figure. the scale factor between the original figure and the scale drawing is 1/3.

a. create a scale drawing of quadrilateral efgh by using a scale factor of 1/2. label this drawing quadrilateral wxyz.
b. draw the original figure. label the resulting quadrilateral abcd.

Explanation:

Step1: Recall scale - factor concept

To create a new scale - drawing with a scale factor of $\frac{1}{2}$, we multiply the side - lengths of quadrilateral EFGH by $\frac{1}{2}$.
The side - lengths of EFGH are: $EF = 1$, $FG=2$, $GH = 4$, and we can find $EH$ using the Pythagorean theorem. For the right - triangle formed by the horizontal and vertical displacements from E to H, the horizontal displacement is 3 and the vertical displacement is 2, so $EH=\sqrt{3^{2}+2^{2}}=\sqrt{9 + 4}=\sqrt{13}$.

Step2: Calculate new side - lengths for WXYZ

$WX=\frac{1}{2}\times EF=\frac{1}{2}\times1=\frac{1}{2}$
$XY=\frac{1}{2}\times FG=\frac{1}{2}\times2 = 1$
$YZ=\frac{1}{2}\times GH=\frac{1}{2}\times4 = 2$
$WZ=\frac{1}{2}\times EH=\frac{\sqrt{13}}{2}$
We then draw quadrilateral WXYZ on the grid with these side - lengths.

Step3: Calculate side - lengths for the original figure ABCD

Since the scale factor from the original figure to EFGH is $\frac{1}{3}$, to get the side - lengths of the original figure ABCD, we multiply the side - lengths of EFGH by 3.
$AB = 3\times EF=3\times1 = 3$
$BC = 3\times FG=3\times2 = 6$
$CD = 3\times GH=3\times4 = 12$
$AD = 3\times EH=3\sqrt{13}$
We then draw quadrilateral ABCD on the grid with these side - lengths.

Since this is a drawing problem, the actual drawing cannot be provided in text. But the steps to calculate the side - lengths for the required scale - drawings are as above.

Answer:

For part a: Calculate side - lengths $WX=\frac{1}{2}$, $XY = 1$, $YZ = 2$, $WZ=\frac{\sqrt{13}}{2}$ and draw quadrilateral WXYZ.
For part b: Calculate side - lengths $AB = 3$, $BC = 6$, $CD = 12$, $AD = 3\sqrt{13}$ and draw quadrilateral ABCD.