draw the image of the following triangle after a dilation centered at the origin with a scale factor of 2.
draw the image of the following triangle after a dilation centered at the origin with a scale factor of 2.
Answer
Explanation:
Step1: Identify original vertices
First, find the coordinates of the original triangle's vertices. Let's assume the original vertices (from the graph) are, for example, ( (6, 8) ), ( (8, 8) ), and ( (7, 5) ) (we'll confirm via grid: each square is 1 unit).
Step2: Apply dilation rule
Dilation centered at the origin with scale factor ( k = 2 ) means each coordinate ( (x, y) ) becomes ( (k \cdot x, k \cdot y) ).
- For ( (6, 8) ): New coordinate is ( (2 \cdot 6, 2 \cdot 8) = (12, 16) )
- For ( (8, 8) ): New coordinate is ( (2 \cdot 8, 2 \cdot 8) = (16, 16) )
- For ( (7, 5) ): New coordinate is ( (2 \cdot 7, 2 \cdot 5) = (14, 10) )
Step3: Plot new vertices
Plot the points ( (12, 16) ), ( (16, 16) ), and ( (14, 10) ) on the grid and connect them to form the dilated triangle.
Answer:
The dilated triangle has vertices at ( (12, 16) ), ( (16, 16) ), and ( (14, 10) ) (plotted and connected on the grid as per the dilation rule).