Question

1. match each transformation with the correct description

a. (x,y)→(3x,y)
b. (x,y)→(x + 3,y)
c. (x,y)→(x,3y)
d. (x,y)→(x,y + 3)
e. (x,y)→(3x,3y)
—— dilation with scale factor 3
—— translation 3 units up
—— translation 3 units right
—— horizontal stretch by a factor of 3
—— vertical stretch by a factor of 3

Explanation:

Step1: Analyze transformation A

$(x,y)\to(3x,y)$ multiplies the $x$ - coordinate by 3, which is a horizontal stretch by a factor of 3.

Step2: Analyze transformation B

$(x,y)\to(x + 3,y)$ adds 3 to the $x$ - coordinate, which is a translation 3 units right.

Step3: Analyze transformation C

$(x,y)\to(x,3y)$ multiplies the $y$ - coordinate by 3, which is a vertical stretch by a factor of 3.

Step4: Analyze transformation D

$(x,y)\to(x,y + 3)$ adds 3 to the $y$ - coordinate, which is a translation 3 units up.

Step5: Analyze transformation E

$(x,y)\to(3x,3y)$ multiplies both $x$ and $y$ - coordinates by 3, which is a dilation with scale factor 3.

Answer:

A. horizontal stretch by a factor of 3
B. translation 3 units right
C. vertical stretch by a factor of 3
D. translation 3 units up
E. dilation with scale factor 3