Question

1. triangle fgh is dilated on a coordinate grid using the origin as the center of the dilation to create triangle fgh. determine if each dilation creates a new triangle fgh that is smaller or larger than the original triangle fgh. write the letter for each rule in the appropriate box.

a. (x,y)→(0.8x,0.8y)
b. (x,y)→(1/3x,1/3y)
c. (x,y)→(2x,2y)
d. (x,y)→(4/3x,4/3y)

1. choose all that give the correct coordinates of the vertices after a dilation of the rectangle tuvw by a scale factor of 4, centered at the origin.

Explanation:

Step1: Recall dilation rule

If the scale - factor \(k\) of a dilation centered at the origin \((x,y)\to(kx,ky)\) and \(0 < k<1\), the image is smaller than the pre - image. If \(k > 1\), the image is larger than the pre - image.

Step2: Analyze Option A

For \((x,y)\to(0.8x,0.8y)\), the scale factor \(k = 0.8\). Since \(0<0.8 < 1\), the new triangle is smaller.

Step3: Analyze Option B

For \((x,y)\to(\frac{1}{3}x,\frac{1}{3}y)\), the scale factor \(k=\frac{1}{3}\). Since \(0<\frac{1}{3}<1\), the new triangle is smaller.

Step4: Analyze Option C

For \((x,y)\to(2x,2y)\), the scale factor \(k = 2\). Since \(2>1\), the new triangle is larger.

Step5: Analyze Option D

For \((x,y)\to(\frac{4}{3}x,\frac{4}{3}y)\), the scale factor \(k=\frac{4}{3}\). Since \(\frac{4}{3}>1\), the new triangle is larger.

Answer:

New triangle is smaller: A. \((x,y)\to(0.8x,0.8y)\), B. \((x,y)\to(\frac{1}{3}x,\frac{1}{3}y)\)
New triangle is larger: C. \((x,y)\to(2x,2y)\), D. \((x,y)\to(\frac{4}{3}x,\frac{4}{3}y)\)