Question

1. dilation rules with quadrilaterals 5a. a quadrilateral is dilated from the origin with a scale factor of 2. which rule represents this transformation? a. (x,y)→(2x,2y) b. (x,y)→(x + 2,y + 2) c. (x,y)→(1/2x,1/2y) d. (x,y)→( - x, - y) 5b. a quadrilateral is reduced from the origin by a scale factor of 1/3. which rule applies? a. (x,y)→(3x,3y) b. (x,y)→(1/3x,1/3y) c. (x,y)→(x - 3,y - 3) d. (x,y)→( - x,y) 5c. which rule shows an enlargement of scale factor 4? a. (x,y)→(4x,4y) b. (x,y)→(x + 4,y + 4) c. (x,y)→(1/4x,1/4y) d. (x,y)→( - y,x) 5d. which rule represents a reduction of scale factor 1/2? a. (x,y)→(1/2x,1/2y) b. (x,y)→(x - 1/2,y - 1/2) c. (x,y)→(2x,2y) d. (x,y)→( - x, - y)

Explanation:

Step1: Recall dilation rule

For a dilation with scale factor $k$ centered at the origin, the rule for a point $(x,y)$ is $(x,y)\to(kx,ky)$.

Step2: Analyze 5a

A dilation with scale factor 2 centered at the origin has the rule $(x,y)\to(2x,2y)$. So the answer for 5a is A. $(x,y)\to(2x,2y)$.

Step3: Analyze 5b

A reduction with scale factor $\frac{1}{3}$ centered at the origin has the rule $(x,y)\to(\frac{1}{3}x,\frac{1}{3}y)$. So the answer for 5b is B. $(x,y)\to(\frac{1}{3}x,\frac{1}{3}y)$.

Step4: Analyze 5c

An enlargement with scale factor 4 centered at the origin has the rule $(x,y)\to(4x,4y)$. So the answer for 5c is A. $(x,y)\to(4x,4y)$.

Step5: Analyze 5d

A reduction with scale factor $\frac{1}{2}$ centered at the origin has the rule $(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)$. So the answer for 5d is A. $(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)$.

Answer:

5a. A. $(x,y)\to(2x,2y)$
5b. B. $(x,y)\to(\frac{1}{3}x,\frac{1}{3}y)$
5c. A. $(x,y)\to(4x,4y)$
5d. A. $(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)$