Question

1. quadrilateral abcd is shown in the coordinate plane below. draw an image of quadrilateral abcd on the coordinate plane using a translation, label the image as efgh and describe the rule you used.

Explanation:

Step1: Assume a translation rule

Let's assume the translation rule is $(x,y)\to(x + 3,y+2)$. This is an arbitrary choice for demonstration purposes.

Step2: Find coordinates of vertices of ABCD

Suppose the coordinates of the vertices of quadrilateral ABCD are $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$ and $D(x_4,y_4)$. For example, if $A(1,1)$, $B(3,1)$, $C(4, - 1)$ and $D(1,-1)$.

Step3: Apply the translation rule to each vertex

For point $A$: $A'(x_1 + 3,y_1+2)=(1 + 3,1 + 2)=(4,3)$
For point $B$: $B'(x_2 + 3,y_2+2)=(3 + 3,1 + 2)=(6,3)$
For point $C$: $C'(x_3 + 3,y_3+2)=(4 + 3,-1 + 2)=(7,1)$
For point $D$: $D'(x_4 + 3,y_4+2)=(1 + 3,-1 + 2)=(4,1)$
Label these new - points as $E,F,G,H$ respectively.
The rule used is $(x,y)\to(x + 3,y + 2)$ which means moving each point 3 units to the right and 2 units up.

Answer:

The image EFGH has vertices found by applying the rule $(x,y)\to(x + 3,y + 2)$ to the vertices of ABCD. For example, if $A(1,1)$, $B(3,1)$, $C(4,-1)$ and $D(1,-1)$, then $E(4,3)$, $F(6,3)$, $G(7,1)$ and $H(4,1)$. The rule is a translation 3 units to the right and 2 units up.