Translation Components 81Cc37

1. **State the problem:** We are given a point $P = (-3, -4)$ and a translation that moves $P$ to a new point $P'$. We need to find the translation components and the coordinates of $P'$. 2. **Identify the translation components:** From the graph description, the point $P$ moves from $(-3, -4)$ to approximately $(-1, -1)$. The translation components are the horizontal and vertical shifts. 3. **Calculate the horizontal translation component:** $$\text{Horizontal shift} = x_{P'} - x_P = -1 - (-3) = -1 + 3 = 2$$ 4. **Calculate the vertical translation component:** $$\text{Vertical shift} = y_{P'} - y_P = -1 - (-4) = -1 + 4 = 3$$ 5. **Write the translation vector:** $$\text{Translation} = (2, 3)$$ 6. **Find the coordinates of $P'$:** $$P' = (x_P + 2, y_P + 3) = (-3 + 2, -4 + 3) = (-1, -1)$$ **Final answer:** Translation components: $(2, 3)$ $P' = (-1, -1)$