Question

the figure below is dilated by a factor of 1/3 centered at the origin. plot the resulting image. click twice to plot a segment. click a segment to delete it.

Explanation:

Step1: Recall dilation formula

If a point $(x,y)$ is dilated by a 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 points

Suppose the coordinates of point $Q$ are $(x_Q,y_Q)$, of point $P$ are $(x_P,y_P)$, of point $O$ are $(x_O,y_O)$, of point $N$ are $(x_N,y_N)$ and of point $M$ are $(x_M,y_M)$.

Step3: Calculate new coordinates

The new coordinates of $Q$: $Q'=(\frac{1}{3}x_Q,\frac{1}{3}y_Q)$. The new coordinates of $P$: $P'=(\frac{1}{3}x_P,\frac{1}{3}y_P)$. The new coordinates of $O$: $O'=(\frac{1}{3}x_O,\frac{1}{3}y_O)$. The new coordinates of $N$: $N'=(\frac{1}{3}x_N,\frac{1}{3}y_N)$. The new coordinates of $M$: $M'=(\frac{1}{3}x_M,\frac{1}{3}y_M)$.

Step4: Plot new points

Plot the points $Q'$, $P'$, $O'$, $N'$, $M'$ on the coordinate - plane and connect them in the same order as the original figure to get the dilated image.

Since the original coordinates of the points are not given, the general way to solve this problem is as above. If you know the specific coordinates of points $Q$, $P$, $O$, $N$, $M$, you can substitute them into the formula $(x',y') = (\frac{1}{3}x,\frac{1}{3}y)$ to get the exact coordinates of the dilated points for plotting.

Answer:

Plot the new points obtained by multiplying the $x$ and $y$ - coordinates of the original points by $\frac{1}{3}$ and connect them in the same order as the original figure.