Question

determine if △abc maps to △xyz. give the dilation in algebraic notation if so.
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 the transformation to A

The transformation is \((x,y)\to(-x,-y)\). For \(A(0,0)\), substituting \(x = 0\), \(y = 0\) gives \((-0,-0)=(0,0)\), which is \(X(0,0)\).

Step2: Apply the transformation to B

For \(B(1,3)\), substituting \(x = 1\), \(y = 3\) gives \((-1,-3)\). But \(Y\) is \((3,9)\), so \((-1,-3)
eq(3,9)\).

Step3: Conclusion

Since the transformation of \(B\) does not match \(Y\), \(\triangle ABC\) does not map to \(\triangle XYZ\) under the given dilation (reflection actually, but checking the mapping) as the transformed \(B\) is not \(Y\).

Answer:

\(\triangle ABC\) does not map to \(\triangle XYZ\) under the transformation \((x,y)\to(-x,-y)\)