Question

a(0, 0), b(1, 3), c(-1, 4)\\
x(0, 0), y(3, 9), z(-2, 8)\\
(x,y)→(-x,-y)

Explanation:

Step1: Apply transformation to A

Given \( A(0,0) \) and transformation \( (x,y)\to(-x,-y) \), substitute \( x = 0,y = 0 \). So \( (-0,-0)=(0,0) \).

Step2: Apply transformation to B

For \( B(1,3) \), substitute \( x = 1,y = 3 \). Then \( (-1,-3) \).

Step3: Apply transformation to C

For \( C(-1,4) \), substitute \( x=-1,y = 4 \). Then \( (-(-1),-4)=(1,-4) \).

Step4: Apply transformation to X

For \( X(0,0) \), substitute \( x = 0,y = 0 \). Then \( (-0,-0)=(0,0) \).

Step5: Apply transformation to Y

For \( Y(3,9) \), substitute \( x = 3,y = 9 \). Then \( (-3,-9) \).

Step6: Apply transformation to Z

For \( Z(-2,8) \), substitute \( x=-2,y = 8 \). Then \( (-(-2),-8)=(2,-8) \).

Answer:

• Transformed \( A \): \( (0,0) \)
• Transformed \( B \): \( (-1,-3) \)
• Transformed \( C \): \( (1,-4) \)
• Transformed \( X \): \( (0,0) \)
• Transformed \( Y \): \( (-3,-9) \)
• Transformed \( Z \): \( (2,-8) \)