the figure below is dilated by a factor of $\frac{1}{3}$ centered at the origin. plot the resulting…

the figure below is dilated by a factor of $\frac{1}{3}$ centered at the origin. plot the resulting image.\nclick twice to plot a segment.\nclick a segment to delete it.

the figure below is dilated by a factor of $\frac{1}{3}$ centered at the origin. plot the resulting image.\nclick twice to plot a segment.\nclick a segment to delete it.

Answer

Explanation:

Step1: Identify original vertices

Original vertices: $H(-6, -6)$, $I(5, -6)$, $J(3, 9)$

Step2: Apply dilation factor $\frac{1}{3}$

For each vertex $(x,y)$, new point is $\left(\frac{1}{3}x, \frac{1}{3}y\right)$:

  • $H'$: $\left(\frac{1}{3} \times -6, \frac{1}{3} \times -6\right) = (-2, -2)$
  • $I'$: $\left(\frac{1}{3} \times 5, \frac{1}{3} \times -6\right) = \left(\frac{5}{3}, -2\right)$
  • $J'$: $\left(\frac{1}{3} \times 3, \frac{1}{3} \times 9\right) = (1, 3)$

Step3: Plot and connect new points

Connect $H'(-2,-2)$, $I'\left(\frac{5}{3},-2\right)$, $J'(1,3)$ to form the dilated triangle.

Answer:

The dilated triangle has vertices at $(-2, -2)$, $\left(\frac{5}{3}, -2\right)$, and $(1, 3)$. Plot these points and connect them in order to get the resulting image.