Question

triangle abc is formed using the translation (x + 0, y + 2) and the dilation by a scale factor of 2 from the origin. which equation explains the relationship between \\(\overline{ac}\\) and \\(\overline{ac}\\)? image of a grid with triangle abc options: \\(\frac{ac}{ac} = 2\\), \\(\frac{ac}{ac} = \frac{1}{2}\\), \\(ac = \frac{ac}{2}\\), \\(\frac{ac}{ac} = 2\\)

Explanation:

Step1: Recall the property of dilation

When a figure is dilated by a scale factor \(k\) from the origin, the length of each side of the new figure is \(k\) times the length of the corresponding side of the original figure. Here, the scale factor \(k = 2\).

Step2: Analyze the relationship between \(AC\) and \(A''C''\)

If the original side length is \(AC\) and the dilated side length is \(A''C''\), then the formula for the relationship between them is \(A''C''=k\times AC\). Since \(k = 2\), we can rewrite it as \(\frac{A''C''}{AC}=2\).

Answer:

\(\frac{A''C''}{AC}=2\) (the first option)