Question

Graph △ DEF and its image after a dilation centered at the given point using the given scale factor. D(0,-4), E(4,0), F(4,-4); dilation centered at point D with a scale facter of 1/2

Answer 1

To dilate triangle DEF centered at D with a scale factor of 1/2, plot the original triangle, keep D at its location, then calculate new coordinates for E and F by halving the distances from D, and plot the new triangle using these points.

Step-by-step explanation:

The question involves performing a dilation of triangle DEF with vertices D(0,-4), E(4,0), and F(4,-4) using a scale factor of 1/2 and centered at point D. To graph the image after dilation, follow these steps:

1. Plot the original triangle DEF on the coordinate plane.

2. Since the dilation is centered at point D and D is the origin of our dilation (D has coordinates of (0,-4)), D will remain fixed.

3. Calculate the coordinates of the other two vertices (E and F) after the dilation. Multiply the distances from point D to points E and F by the scale factor of 1/2.

4. E is 4 units to the right and 4 units up from D. Half of these distances is 2, so the image of E after dilation will be E' at (2,-2).

5. F is directly to the right of D by 4 units. Half of this distance is 2, so the image of F after dilation will be F' at (2,-4).

6. Connect the new points D, E', and F' to form the dilated triangle DEF'.

7. Label the new triangle on the graph for clarity.

The process shows how using a center of dilation and a scale factor can effectively shrink or enlarge geometric figures in a proportional manner.