Question

graph the image of the jklm after a dilation with a scale - factor of 1/2 centered at the origin. label the appropriate vertices as jklm.

Explanation:

Step1: Recall dilation formula

If a point $(x,y)$ is dilated with a scale - factor $k$ centered at the origin, the new point $(x',y')$ is given by $(x',y')=(kx,ky)$. Here $k = \frac{1}{3}$.

Step2: Assume coordinates of vertices

Let's assume the vertices of the quadrilateral $JKLM$ have coordinates $J(x_J,y_J)$, $K(x_K,y_K)$, $L(x_L,y_L)$, $M(x_M,y_M)$. After dilation, the new vertices $J'(x_{J'},y_{J'})$, $K'(x_{K'},y_{K'})$, $L'(x_{L'},y_{L'})$, $M'(x_{M'},y_{M'})$ will be $J'( \frac{1}{3}x_J,\frac{1}{3}y_J)$, $K'( \frac{1}{3}x_K,\frac{1}{3}y_K)$, $L'( \frac{1}{3}x_L,\frac{1}{3}y_L)$, $M'( \frac{1}{3}x_M,\frac{1}{3}y_M)$.

Step3: Plot new points

Locate the new points $J'$, $K'$, $L'$, $M'$ on the coordinate - grid and connect them in the same order as the original quadrilateral $JKLM$ to get the dilated image.

Since the original coordinates of the vertices of $JKLM$ are not given explicitly, the general procedure for graphing the dilated image is as above. If we had the actual coordinates of the vertices of $JKLM$, for example, if $J=(x_1,y_1)$, then $J'=(\frac{1}{3}x_1,\frac{1}{3}y_1)$. We would repeat this process for all vertices and then graph the new quadrilateral.

Answer:

Step1: Recall dilation formula

If a point $(x,y)$ is dilated with a scale - factor $k$ centered at the origin, the new point $(x',y')$ is given by $(x',y')=(kx,ky)$. Here $k = \frac{1}{3}$.

Step2: Assume coordinates of vertices

Let's assume the vertices of the quadrilateral $JKLM$ have coordinates $J(x_J,y_J)$, $K(x_K,y_K)$, $L(x_L,y_L)$, $M(x_M,y_M)$. After dilation, the new vertices $J'(x_{J'},y_{J'})$, $K'(x_{K'},y_{K'})$, $L'(x_{L'},y_{L'})$, $M'(x_{M'},y_{M'})$ will be $J'( \frac{1}{3}x_J,\frac{1}{3}y_J)$, $K'( \frac{1}{3}x_K,\frac{1}{3}y_K)$, $L'( \frac{1}{3}x_L,\frac{1}{3}y_L)$, $M'( \frac{1}{3}x_M,\frac{1}{3}y_M)$.

Step3: Plot new points

Locate the new points $J'$, $K'$, $L'$, $M'$ on the coordinate - grid and connect them in the same order as the original quadrilateral $JKLM$ to get the dilated image.

Since the original coordinates of the vertices of $JKLM$ are not given explicitly, the general procedure for graphing the dilated image is as above. If we had the actual coordinates of the vertices of $JKLM$, for example, if $J=(x_1,y_1)$, then $J'=(\frac{1}{3}x_1,\frac{1}{3}y_1)$. We would repeat this process for all vertices and then graph the new quadrilateral.