Question

graph the image of rectangle klmn after a translation 4 units left and 9 units down.

Explanation:

Step1: Recall translation rule

For a point $(x,y)$ translated $a$ units left and $b$ units down, the new - point is $(x - a,y - b)$. Here $a = 4$ and $b = 9$.

Step2: Identify coordinates of rectangle vertices

Assume $K(-2,1)$, $L(8,1)$, $M(8,7)$, $N(-2,7)$.

Step3: Translate point $K$

For $K(-2,1)$, the new $x$ - coordinate is $x=-2 - 4=-6$, and the new $y$ - coordinate is $y = 1-9=-8$. So new $K$ is $(-6,-8)$.

Step4: Translate point $L$

For $L(8,1)$, the new $x$ - coordinate is $x = 8-4 = 4$, and the new $y$ - coordinate is $y=1 - 9=-8$. So new $L$ is $(4,-8)$.

Step5: Translate point $M$

For $M(8,7)$, the new $x$ - coordinate is $x = 8-4 = 4$, and the new $y$ - coordinate is $y=7 - 9=-2$. So new $M$ is $(4,-2)$.

Step6: Translate point $N$

For $N(-2,7)$, the new $x$ - coordinate is $x=-2 - 4=-6$, and the new $y$ - coordinate is $y=7 - 9=-2$. So new $N$ is $(-6,-2)$.

Step7: Graph the new rectangle

Plot the points $(-6,-8)$, $(4,-8)$, $(4,-2)$, $(-6,-2)$ and connect them to form the new rectangle.

Answer:

Graph the rectangle with vertices $(-6,-8)$, $(4,-8)$, $(4,-2)$, $(-6,-2)$.