Question

1. quadrilateral abcd is shown on the coordinate plane. a. draw the image of quadrilateral abcd after a translation that takes a to a. label the image abcd. b. draw the image of quadrilateral abcd after a rotation 90° clockwise around the origin. label the image abcd.

Explanation:

Step1: Find translation vector

The coordinates of $A=(1,1)$ and $A'=(- 4,1)$. The translation vector is $(-4 - 1,1 - 1)=(-5,0)$. To find the new coordinates of $B=(3,1)$, $C=(4,4)$ and $D=(2,4)$, we add the translation vector to their original coordinates. For $B$, the new - coordinates $B'=(3-5,1)=(-2,1)$. For $C$, $C'=(4 - 5,4)=(-1,4)$. For $D$, $D'=(2-5,4)=(-3,4)$. Then we draw and label the quadrilateral $A'B'C'D'$.

Step2: Apply rotation rule

The rule for a $90^{\circ}$ clock - wise rotation around the origin is $(x,y)\to(y,-x)$. For $A=(1,1)$, $A''=(1,-1)$. For $B=(3,1)$, $B''=(1,-3)$. For $C=(4,4)$, $C''=(4,-4)$. For $D=(2,4)$, $D''=(4,-2)$. Then we draw and label the quadrilateral $A''B''C''D''$.

Since this is a drawing problem, we can't provide the actual drawing in text - based format. But the steps above give the coordinates for the new points after translation and rotation. The process of finding the new coordinates for each vertex of the quadrilateral is the key to solving this problem.

Answer:

For part a: The coordinates of $A'(-4,1)$, $B'(-2,1)$, $C'(-1,4)$, $D'(-3,4)$ are used to draw the translated quadrilateral.
For part b: The coordinates of $A''(1,-1)$, $B''(1,-3)$, $C''(4,-4)$, $D''(4,-2)$ are used to draw the rotated quadrilateral.