Question

parallelogram abcd is rotated to create image abcd. which rule describes the transformation? options: (x,y) → (y, -x); (x,y) → (-y, x); (x,y) → (-x, -y); (x,y) → (x, -y)

Explanation:

Step1: Identify coordinates of point A

Original point $A$: $(1, 5)$; Image point $A'$: $(5, -1)$

Step2: Test each transformation rule

• Rule 1: $(x,y)\to(y,-x)$: $(1,5)\to(5,-1)$ (matches $A\to A'$)
• Rule 2: $(x,y)\to(-y,x)$: $(1,5)\to(-5,1)$ (does not match)
• Rule 3: $(x,y)\to(-x,-y)$: $(1,5)\to(-1,-5)$ (does not match)
• Rule 4: $(x,y)\to(x,-y)$: $(1,5)\to(1,-5)$ (does not match)

Step3: Verify with another point (e.g., B)

Original point $B$: $(5, 4)$; Image point $B'$: $(4, -5)$
Apply Rule 1: $(5,4)\to(4,-5)$ (matches $B\to B'$)

Answer:

$(x, y) \to (y, -x)$