Subjects geometry

Figure Translation

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Figure Translation


1. **State the problem:** We need to determine which translation(s) map Figure O onto Figure P on the coordinate plane. 2. **Understand translation:** A translation moves every point of a figure the same distance in the same direction. The translation vector is given by $$\vec{v} = (\Delta x, \Delta y)$$ where $$\Delta x$$ is the horizontal shift and $$\Delta y$$ is the vertical shift. 3. **Identify coordinates:** Approximate the center of Figure O and Figure P. - Figure O center: approximately at $$(-5.5, 6.5)$$ - Figure P center: approximately at $$(-9.5, -3.5)$$ 4. **Calculate translation vector:** $$\Delta x = x_{P} - x_{O} = -9.5 - (-5.5) = -4$$ $$\Delta y = y_{P} - y_{O} = -3.5 - 6.5 = -10$$ 5. **Interpretation:** The translation vector that maps Figure O onto Figure P is $$\vec{v} = (-4, -10)$$. 6. **Check translation:** Applying this vector to all vertices of Figure O should move it exactly onto Figure P. **Final answer:** The translation that maps Figure O onto Figure P is a shift left by 4 units and down by 10 units, or $$\boxed{(-4, -10)}$$.