Question

graph the image of kite (jklm) after a dilation with a scale factor of (\frac{1}{4}), centered at the origin. match the appropriate coordinate for (jklm).

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor $k$, if a point $(x,y)$ is dilated, the new point $(x',y')$ is given by $(x',y')=(k x,k y)$. Here $k = \frac{1}{4}$.

Step2: Assume coordinates of point $J$

Let's assume the coordinates of point $J$ are $(x_J,y_J)$. From the graph, if we assume $J=(4, - 8)$ (by looking at the grid - intersection where $J$ lies).

Step3: Calculate coordinates of $J'$

Using the dilation formula, $x_{J'}=\frac{1}{4}x_J$ and $y_{J'}=\frac{1}{4}y_J$. Substituting $x_J = 4$ and $y_J=-8$, we get $x_{J'}=\frac{1}{4}\times4 = 1$ and $y_{J'}=\frac{1}{4}\times(-8)=-2$. So the coordinates of $J'$ are $(1,-2)$.

Answer:

$(1,-2)$