The problem asks for the coordinates of the vertices after a dilation with a scale factor of 5 about the origin. A dilation transforms each point by multiplying its coordinates by the scale factor.

Let's first identify the original coordinates of points $B$, $C$, $D$, and $E$:

• $B(-2, -2)$
• $C(-2, 2)$
• $D(2, 2)$
• $E(2, -2)$

Now, apply the dilation by multiplying both the $x$- and $y$-coordinates of each point by the scale factor of 5.

1. For $B(-2, -2)$: $B' = (-2 \times 5, -2 \times 5) = (-10, -10)$

2. For $C(-2, 2)$: $C' = (-2 \times 5, 2 \times 5) = (-10, 10)$

3. For $D(2, 2)$: $D' = (2 \times 5, 2 \times 5) = (10, 10)$

4. For $E(2, -2)$: $E' = (2 \times 5, -2 \times 5) = (10, -10)$

Thus, the new coordinates are:

• $B'(-10, -10)$
• $C'(-10, 10)$
• $D'(10, 10)$
• $E'(10, -10)$

Would you like any further details on this dilation process?

Related Questions:

1. What is the effect of using a scale factor less than 1 in dilation?
2. How do you calculate dilation when the center is not the origin?
3. What happens to shapes after dilation in terms of angle measures and side ratios?
4. How do you perform a dilation when the center is outside the shape?
5. Can dilation ever change the orientation of a shape?

Tip: Dilation about the origin preserves the shape but scales the size and distance from the origin proportionally.