Question

graph the image of rectangle rstu after a dilation with a scale factor of 1/5, centered at the origin.

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 $(x',y')=(k x,k y)$. Here $k = \frac{1}{5}$.

Step2: Assume rectangle vertices

Let's assume the vertices of rectangle $RSTU$ are $R(x_1,y_1)$, $S(x_2,y_2)$, $T(x_3,y_3)$, $U(x_4,y_4)$. From the graph, if we assume $R(- 10,-10)$, $S(10,-10)$, $T(10,5)$, $U(-10,5)$.

Step3: Calculate new vertices

For vertex $R$: $x_R'=\frac{1}{5}\times(-10)=-2$, $y_R'=\frac{1}{5}\times(-10)=-2$.
For vertex $S$: $x_S'=\frac{1}{5}\times10 = 2$, $y_S'=\frac{1}{5}\times(-10)=-2$.
For vertex $T$: $x_T'=\frac{1}{5}\times10 = 2$, $y_T'=\frac{1}{5}\times5 = 1$.
For vertex $U$: $x_U'=\frac{1}{5}\times(-10)=-2$, $y_U'=\frac{1}{5}\times5 = 1$.

Step4: Graph new rectangle

Plot the points $R'(-2,-2)$, $S'(2,-2)$, $T'(2,1)$, $U'(-2,1)$ on the same coordinate - plane and connect them to form the dilated rectangle.

The new rectangle has vertices at approximately $(-2,-2)$, $(2,-2)$, $(2,1)$, $(-2,1)$ (assuming the original rectangle vertices as described above). You would graph these points on the given coordinate grid and connect them to form the dilated rectangle.

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 $(x',y')=(k x,k y)$. Here $k = \frac{1}{5}$.

Step2: Assume rectangle vertices

Let's assume the vertices of rectangle $RSTU$ are $R(x_1,y_1)$, $S(x_2,y_2)$, $T(x_3,y_3)$, $U(x_4,y_4)$. From the graph, if we assume $R(- 10,-10)$, $S(10,-10)$, $T(10,5)$, $U(-10,5)$.

Step3: Calculate new vertices

For vertex $R$: $x_R'=\frac{1}{5}\times(-10)=-2$, $y_R'=\frac{1}{5}\times(-10)=-2$.
For vertex $S$: $x_S'=\frac{1}{5}\times10 = 2$, $y_S'=\frac{1}{5}\times(-10)=-2$.
For vertex $T$: $x_T'=\frac{1}{5}\times10 = 2$, $y_T'=\frac{1}{5}\times5 = 1$.
For vertex $U$: $x_U'=\frac{1}{5}\times(-10)=-2$, $y_U'=\frac{1}{5}\times5 = 1$.

Step4: Graph new rectangle

Plot the points $R'(-2,-2)$, $S'(2,-2)$, $T'(2,1)$, $U'(-2,1)$ on the same coordinate - plane and connect them to form the dilated rectangle.

The new rectangle has vertices at approximately $(-2,-2)$, $(2,-2)$, $(2,1)$, $(-2,1)$ (assuming the original rectangle vertices as described above). You would graph these points on the given coordinate grid and connect them to form the dilated rectangle.