Question

draw the image of the following triangle after a dilation centered at the origin with a scale factor of \\(\frac{1}{2}\\).

Explanation:

Step1: Identify Original Triangle Coordinates

Assume the original triangle has vertices (let's estimate from the grid). Suppose the top vertex is at (6, 8), bottom left at (4, 12), bottom right at (8, 12).

Step2: Apply Dilation (Scale Factor \( \frac{1}{2} \))

For a dilation centered at the origin \((0,0)\), the new coordinates \((x', y')\) are given by \( x' = \frac{1}{2}x \), \( y' = \frac{1}{2}y \).

• For (6, 8): \( x' = \frac{1}{2} \times 6 = 3 \), \( y' = \frac{1}{2} \times 8 = 4 \)
• For (4, 12): \( x' = \frac{1}{2} \times 4 = 2 \), \( y' = \frac{1}{2} \times 12 = 6 \)
• For (8, 12): \( x' = \frac{1}{2} \times 8 = 4 \), \( y' = \frac{1}{2} \times 12 = 6 \)

Step3: Plot New Vertices

Plot the new vertices (3, 4), (2, 6), (4, 6) on the grid to get the dilated triangle.

Answer:

The dilated triangle has vertices at (3, 4), (2, 6), and (4, 6) (plotted on the grid as per the dilation rules).