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) why did i choose b as my correct answer. was i right? how have i gotten that answer?

Explanation:

Step1: Identify original coordinates of B

Assume the original rectangle has vertices with B having coordinates (3, 5) (since the card measures 3 inches by 5 inches and we can infer the position of B based on the rectangle - like shape).

Step2: Apply dilation formula

For a dilation with scale - factor \(k = 2\) and center of dilation at the origin \((0,0)\), the formula for the coordinates of a point \((x,y)\) after dilation is \((kx,ky)\). Here \(x = 3\) and \(y = 5\), so \(x'=2\times3 = 6\) and \(y'=2\times5 = 10\).

Answer:

D. (6, 10)