Question

x(-2, 5) → x(-4, 10) y(4, 3) → y(8, 6) z(-3, -5) → z(-6, -10) (b) choose the general rule below that describes the dilation mapping △xyz to △xyz. options: (x, y) → (2x, y); (x, y) → (2x, 2y); (x, y) → (left(\frac{1}{2}x, 2y
ight)); (x, y) → (left(\frac{1}{2}x, \frac{1}{2}y
ight)); (x, y) → (left(\frac{1}{2}y, \frac{1}{2}x
ight)); (x, y) → (x, 2y); (x, y) → (2y, 2x); (x, y) → (left(2x, \frac{1}{2}y
ight))

Explanation:

Step1: Analyze X-coordinate transformation

For point \( X(-2, 5) \to X'(-4, 10) \), the x - coordinate changes from \(-2\) to \(-4\). We calculate the scale factor for x - coordinate: \(\frac{-4}{-2}=2\).
For point \( Y(4, 3) \to Y'(8, 6) \) (wait, the problem says \( Y(4,3)\to Y'(8,6) \)? Wait, the user's image shows \( Y(4,3)\to Y'(8,6) \)? Wait, the user's text in the image: \( X(-2,5)\to X'(-4,10) \), \( Y(4,3)\to Y'(8,6) \), \( Z(-3,-5)\to Z'(-6,-10) \). Let's check x - coordinate: \(\frac{-4}{-2} = 2\), \(\frac{8}{4}=2\), \(\frac{-6}{-3}=2\).

Step2: Analyze Y - coordinate transformation

For y - coordinate: \(\frac{10}{5}=2\), \(\frac{6}{3}=2\), \(\frac{-10}{-5}=2\). So the transformation rule is \((x,y)\to(2x,2y)\).

Answer:

\((x,y)\to(2x,2y)\) (the option with this rule)