Question

graph the image of kite bcde after a dilation with a scale factor of \\(\frac{1}{4}\\), centered at the origin.

Explanation:

Step1: Identify coordinates of kite vertices

From graph: \( B(0,-8) \), \( C(4,-4) \), \( D(0,4) \), \( E(-4,-4) \)

Step2: Apply dilation rule (scale factor \( \frac{1}{4} \), origin center)

New coordinates: \( (x \times \frac{1}{4}, y \times \frac{1}{4}) \)

• \( B'(0 \times \frac{1}{4}, -8 \times \frac{1}{4}) = (0, -2) \)
• \( C'(4 \times \frac{1}{4}, -4 \times \frac{1}{4}) = (1, -1) \)
• \( D'(0 \times \frac{1}{4}, 4 \times \frac{1}{4}) = (0, 1) \)
• \( E'(-4 \times \frac{1}{4}, -4 \times \frac{1}{4}) = (-1, -1) \)

Step3: Plot new vertices and connect

Draw polygon with \( B'(0,-2) \), \( C'(1,-1) \), \( D'(0,1) \), \( E'(-1,-1) \)

Answer:

The image of kite \( BCDE \) after dilation has vertices at \( (0,-2) \), \( (1,-1) \), \( (0,1) \), and \( (-1,-1) \), forming a smaller kite centered at the origin.