Question

write a coordinate rule for the dilation.

Explanation:

Step1: Find coordinates of corresponding points

Find coordinates of \(B(2,1)\) and \(B'(4,3)\), \(C(2,0)\) and \(C'(6,0)\).

Step2: Calculate the scale factor for \(x\) and \(y\) - coordinates

For \(x\) - coordinate: \(\frac{4}{2}=2\), \(\frac{6}{2} = 3\) (wait, no, correct: take \(C(2,0)\) and \(C'(6,0)\), \(x\) - scale factor \(k_x=\frac{6 - 2}{2-2}\) (wrong approach). Correct approach: take a point \(A(2,-1)\) (assuming from graph) and \(A'(4,-3)\). Wait, no, better: take \(B(1,1)\) (assuming original triangle \(ABC\) with \(A(1,-1)\), \(B(1,1)\), \(C(2,0)\) and \(A'(3,-3)\), \(B'(3,3)\), \(C'(6,0)\). Wait no, re - check:
Original triangle: assume \(A(1,-1)\), \(B(1,1)\), \(C(2,0)\). Dilated triangle: \(A'(3,-3)\), \(B'(3,3)\), \(C'(6,0)\).
For \(x\) - coordinate: \(\frac{3}{1}=3\), \(\frac{6}{2}=3\). For \(y\) - coordinate: \(\frac{3}{1}=3\), \(\frac{- 3}{-1}=3\).

Answer:

\((x,y)\to(3x,3y)\)