Question

10 graph the image of kite jklm after a dilation with a scale - factor of 1/4, centered at the origin. match the appropriate coordinate to jklm.

Explanation:

Step1: Recall dilation formula

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

Step2: Assume coordinates of kite vertices

Let's assume the coordinates of the vertices of kite $JKLM$ are $J(x_J,y_J)$, $K(x_K,y_K)$, $L(x_L,y_L)$, $M(x_M,y_M)$. After dilation, the coordinates of the vertices of the image $J'K'L'M'$ will be $J'(\frac{1}{4}x_J,\frac{1}{4}y_J)$, $K'(\frac{1}{4}x_K,\frac{1}{4}y_K)$, $L'(\frac{1}{4}x_L,\frac{1}{4}y_L)$, $M'(\frac{1}{4}x_M,\frac{1}{4}y_M)$.

Step3: Calculate new coordinates

Since the problem does not give the original coordinates of the vertices of the kite, in general, if a vertex of the original kite has coordinates $(x,y)$, the coordinates of the corresponding vertex of the dilated kite are $(\frac{x}{4},\frac{y}{4})$. For example, if a vertex is $(8,0)$, after dilation with a scale - factor of $\frac{1}{4}$ centered at the origin, the new vertex is $(\frac{8}{4},\frac{0}{4})=(2,0)$.

Answer:

To find the coordinates of $J'$, $K'$, $L'$, $M'$, take the coordinates of $J$, $K$, $L$, $M$ respectively and multiply each $x$ and $y$ coordinate by $\frac{1}{4}$. Without the original coordinates of $J$, $K$, $L$, $M$, we can't give specific numerical answers for $J'$, $K'$, but the general method is to use the formula $(x',y') = (\frac{1}{4}x,\frac{1}{4}y)$ for each vertex $(x,y)$ of the original kite.