Subjects geometry

Distance Points 6Fdc4D

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Question: Find the distance between the points $(-6, -4)$ and $(-6, 18)$.
1. **State the problem:** We need to find the distance between the points $(-6, -4)$ and $(-6, 18)$. 2. **Formula used:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Apply the formula:** Here, $x_1 = -6$, $y_1 = -4$, $x_2 = -6$, and $y_2 = 18$. Substitute these values: $$d = \sqrt{(-6 - (-6))^2 + (18 - (-4))^2} = \sqrt{(0)^2 + (18 + 4)^2} = \sqrt{0 + 22^2} = \sqrt{484}$$ 4. **Simplify:** $$d = \sqrt{484} = 22$$ 5. **Interpretation:** Since the $x$-coordinates are the same, the points lie on a vertical line, and the distance is simply the difference in the $y$-coordinates, which is $22$ units. **Final answer:** The distance between the points is $22$ units.
(-6, 18)(-6, -4)