Question

plot the image of point c under a dilation about the origin (0,0) with a scale factor of $\frac{1}{5}$.

Explanation:

Step1: Recall dilation formula

If a point $(x,y)$ is dilated about the origin with a scale - factor $k$, the new point $(x',y')$ is given by $(x',y')=(k x,k y)$.

Step2: Assume coordinates of point C

Let's assume the coordinates of point $C$ are $(x_0,y_0)$. From the graph, we can see that $x_0=- 5$ and $y_0 = 5$.

Step3: Calculate new coordinates

The scale - factor $k=\frac{1}{5}$. So, $x'=k x_0=\frac{1}{5}\times(-5)=-1$ and $y'=k y_0=\frac{1}{5}\times5 = 1$.

Answer:

The image of point $C$ has coordinates $(-1,1)$. Plot this point on the graph.