Question

observe and record the coordinates of the transformation shown below. how can this transformation be represented algebraically?
a. $(-x, -y)$
b. $(-y, -x)$
c. $(x, -y)$
d. $(-x, y)$

Explanation:

Step1: Identify original coordinates

Original points: $A(2,-5)$, $B(6,-5)$, $C(2,-2)$

Step2: Identify transformed coordinates

Transformed points: $A'(-2,6)$, $B'(-6,6)$, $C'(-2,3)$

Step3: Test option A on $A$

Apply $(-x,-y)$: $(-2, 5)$ ≠ $A'(-2,6)$ → Invalid

Step4: Test option B on $A$

Apply $(-y,-x)$: $(-(-5), -2)=(5,-2)$ ≠ $A'(-2,6)$ → Invalid

Step5: Test option C on $A$

Apply $(x,-y)$: $(2,5)$ ≠ $A'(-2,6)$ → Invalid

Step6: Test option D on $A$

Apply $(-x,y)$: $(-2,-(-5))=(-2,6)=A'$

Step7: Verify option D on $B$

Apply $(-x,y)$: $(-6,-(-5))=(-6,6)=B'$

Step8: Verify option D on $C$

Apply $(-x,y)$: $(-2,-(-2))=(-2,2)=C'$

Answer:

D. $(-x, y)$