Question

determine the coordinates of the afterimage. is this an enlargement or a reduction?
d:(x,y)→(0.5x, 0.5y); a(10, 6), b(8, -4), c(-2, 0)
a = ( )
b = ( )
c = ( )
enlargement or reduction

Explanation:

Step1: Apply transformation to A

The transformation is \((x,y)\to(0.5x, 0.5y)\). For \(A(10,6)\), calculate \(0.5\times10 = 5\) and \(0.5\times6 = 3\). So \(A'=(5,3)\).

Step2: Apply transformation to B

For \(B(8, - 4)\), calculate \(0.5\times8=4\) and \(0.5\times(-4)=-2\). So \(B'=(4,-2)\).

Step3: Apply transformation to C

For \(C(-2,0)\), calculate \(0.5\times(-2)=-1\) and \(0.5\times0 = 0\). So \(C'=(-1,0)\).

Step4: Determine enlargement or reduction

The scale factor is \(0.5\) (since we multiply \(x\) and \(y\) by \(0.5\)). A scale factor between \(0\) and \(1\) indicates a reduction.

Answer:

\(A'=(5,3)\), \(B'=(4, - 2)\), \(C'=(-1,0)\); This is a reduction (scale factor \(0.5\)).