Subjects geometry

Distance Dubai Map A7328F

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1. **Problem Statement:** We are given three locations on a coordinate plane representing a simple city map of Dubai: School at (2, 3), Mall at (2, 8), and Park at (7, 3). We need to find the distances from School to Mall and from School to Park. 2. **Formula Used:** The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ on a coordinate plane is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Distance from School to Mall:** - Coordinates: School $(2, 3)$, Mall $(2, 8)$ - Calculate differences: $$x_2 - x_1 = 2 - 2 = 0$$ $$y_2 - y_1 = 8 - 3 = 5$$ - Substitute into the distance formula: $$d = \sqrt{0^2 + 5^2} = \sqrt{25} = 5$$ 4. **Distance from School to Park:** - Coordinates: School $(2, 3)$, Park $(7, 3)$ - Calculate differences: $$x_2 - x_1 = 7 - 2 = 5$$ $$y_2 - y_1 = 3 - 3 = 0$$ - Substitute into the distance formula: $$d = \sqrt{5^2 + 0^2} = \sqrt{25} = 5$$ 5. **Conclusion:** The distance from School to Mall is 5 units, and the distance from School to Park is also 5 units. These distances represent vertical and horizontal separations on the coordinate plane, respectively.
School (2,3)Mall (2,8)Park (7,3)