Answer:
The vertices of the image are D' (40, 20), E' (10, 30), F' (15, 5)
Step-by-step explanation:
If the point (x, y) dilated by a scale factor k using the origin as a center of dilation, then its image is (kx, ky)
Let us use this rule to solve our question
∵ The vertices of ΔDEF are D (8, 4), E (2, 6), and F (3, 1)
∵ ΔDEF dilated by a scale factor 5
∴ k = 5
∵ The origin as the center of dilation
→ That means, multiply the coordinates of every point by 5
∴ D' = (8 × 5, 4 × 5)
∴ D' = (40, 20)
∴ E' = (2 × 5, 6 × 5)
∴ E' = (10, 30)
∴ F' = (3 × 5, 1 × 5)
∴ D' = (15, 5)
∴ The vertices of the image are D' (40, 20), E' (10, 30), F' (15, 5)
