Question

yolanda and her mom make greeting cards to send to family and friends. yolanda designs a card that measures 3 inches by 5 inches. the card is represented by figure abcd. she enlarges the card to form image abcd. she uses a scale factor of 2 with a center of dilation at the origin. what are the coordinates of b? a (3, 5) b (5, 7) c (6, 5) d (6, 10) wyatt chose b as the correct answer. how might he have gotten that answer?

Explanation:

Step1: Determine original coordinates of B

From the graph, the coordinates of point B are (3, 5).

Step2: Apply dilation formula

For a dilation with scale - factor \(k = 2\) and center of dilation at the origin \((x,y)\to(kx,ky)\). Here \(x = 3\) and \(y = 5\), so \(x'=2\times3 = 6\) and \(y'=2\times5 = 10\).

Step3: Analyze Wyatt's error

Wyatt likely added 2 to each coordinate of B instead of multiplying by 2. He did \((3 + 2,5+2)=(5,7)\).

Answer:

The correct answer is D. (6, 10). Wyatt might have added 2 to each coordinate of B instead of multiplying by the scale - factor 2.