Subjects geometry

Point Translation 020Cd3

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1. **State the problem:** We have four points: (2, 6), (-2, 5), (-3, -10), and (3, 3). Each point undergoes a translation defined by the rule $(x, y) \to (x - 8, y + 4)$. 2. **Formula used:** The translation rule means subtract 8 from the x-coordinate and add 4 to the y-coordinate for each point. 3. **Apply the translation to each point:** - For $(2, 6)$: $$ (2 - 8, 6 + 4) = (-6, 10) $$ - For $(-2, 5)$: $$ (-2 - 8, 5 + 4) = (-10, 9) $$ - For $(-3, -10)$: $$ (-3 - 8, -10 + 4) = (-11, -6) $$ - For $(3, 3)$: $$ (3 - 8, 3 + 4) = (-5, 7) $$ 4. **Match the translated points to the given options:** - $(-6, 10)$ matches the option $(-6, 10)$. - $(-10, 9)$ matches the option $(-10, 9)$. - $(-11, -6)$ matches the option $(-11, -6)$. - $(-5, 7)$ does not match any given option exactly; the closest option is $(-5, 1)$ but the y-coordinate differs. 5. **Conclusion:** The translated points are $(-6, 10)$, $(-10, 9)$, $(-11, -6)$, and $(-5, 7)$, with three matching the provided options exactly.