Question

1. rectangle abcd is dilated using the origin as the center of dilation to create rectangle abcd. which rule best represents the dilation applied to rectangle abcd to create rectangle abcd? a. (x, y)→(x, 8y) b. (x, y)→(3x, 3y) c. (x, y)→(3x, 8y) d. (x, y)→(8x, 3x)

Explanation:

Step1: Recall dilation rule

In a dilation centered at the origin, if the scale - factor is \(k\), the rule for a point \((x,y)\) is \((x,y)\to(kx,ky)\).

Step2: Analyze the options

We need to find the rule that represents a dilation. Option A \((x,y)\to(x, 8y)\) is not a uniform dilation as the \(x\) and \(y\) are scaled differently. Option B \((x,y)\to(3x, - 3y)\) represents a dilation with a scale - factor of \(3\) and a reflection across the origin (due to the negative sign). Option C \((x,y)\to(3x,3y)\) represents a dilation with a scale - factor of \(3\) centered at the origin. Option D \((x,y)\to(9x,3x)\) is not a valid dilation rule as the \(y\) - coordinate is being set equal to a multiple of \(x\) which is not how dilations work.

Answer:

C. \((x,y)\to(3x,3y)\)