Question

graph the image of square klmn after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Recall dilation rule

If a point $(x,y)$ is dilated with a scale - factor $k$ centered at the origin, the new point is $(kx,ky)$. Here $k = 2$.

Step2: Assume coordinates of square vertices

Let's assume the vertices of square $KLMN$ have coordinates, say $K(x_1,y_1)$, $L(x_2,y_2)$, $M(x_3,y_3)$, $N(x_4,y_4)$. For example, if $K(- 3,-5)$, $L(-1,-5)$, $M(-1,-3)$, $N(-3,-3)$.

Step3: Apply dilation formula

For point $K(-3,-5)$, the new point $K'$ after dilation with $k = 2$ is $K'(2\times(-3),2\times(-5))=(-6,-10)$. For $L(-1,-5)$, $L'(2\times(-1),2\times(-5))=(-2,-10)$. For $M(-1,-3)$, $M'(2\times(-1),2\times(-3))=(-2,-6)$. For $N(-3,-3)$, $N'(2\times(-3),2\times(-3))=(-6,-6)$.

Step4: Plot new points

Plot the points $K'$, $L'$, $M'$, $N'$ on the coordinate - plane and connect them to form the dilated square.

Answer:

Plot the new square with vertices obtained by multiplying the coordinates of the original square's vertices by 2 and connecting them.