graph the image of $\triangle pqr$ after a dilation with a scale factor of $\frac{1}{4}$, centered at the…

Explanation:

Step1: Identify original coordinates

$P(-4, 0)$, $Q(8, 0)$, $R(0, -4)$

Step2: Apply dilation formula

For a point $(x,y)$ scaled by $\frac{1}{4}$ from origin: $\left(\frac{1}{4}x, \frac{1}{4}y\right)$

Step3: Calculate new point $P'$

$P'\left(\frac{1}{4}\times(-4), \frac{1}{4}\times0\right) = (-1, 0)$

Step4: Calculate new point $Q'$

$Q'\left(\frac{1}{4}\times8, \frac{1}{4}\times0\right) = (2, 0)$

Step5: Calculate new point $R'$

$R'\left(\frac{1}{4}\times0, \frac{1}{4}\times(-4)\right) = (0, -1)$

Step6: Plot and connect $P', Q', R'$

Connect the three new points to form the dilated triangle.

Answer:

The coordinates of the dilated triangle $\Delta P'Q'R'$ are $P'(-1, 0)$, $Q'(2, 0)$, $R'(0, -1)$. Plot these points and connect them to graph the image.