1. **Problem Statement:** Given the coordinates of four locations on a grid where each unit represents 0.75 miles, find the distances between these locations in miles. 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: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ Since each unit corresponds to 0.75 miles, the actual distance in miles is: $$d_{miles} = 0.75 \times d$$ 3. **Calculate Distance from GROCERY STORE to JIM'S HOUSE:** Coordinates: GROCERY STORE $(-8, 9)$, JIM'S HOUSE $(6, 4)$ $$d = \sqrt{(6 - (-8))^2 + (4 - 9)^2} = \sqrt{(6 + 8)^2 + (-5)^2} = \sqrt{14^2 + 25} = \sqrt{196 + 25} = \sqrt{221}$$ $$d_{miles} = 0.75 \times \sqrt{221} \approx 0.75 \times 14.8661 = 11.15$$ miles 4. **Calculate Distance from BANK to MALL:** Coordinates: BANK $(-9, -3)$, MALL $(-5, -9)$ $$d = \sqrt{(-5 - (-9))^2 + (-9 - (-3))^2} = \sqrt{(4)^2 + (-6)^2} = \sqrt{16 + 36} = \sqrt{52}$$ $$d_{miles} = 0.75 \times \sqrt{52} \approx 0.75 \times 7.2111 = 5.41$$ miles 5. **Calculate Distance from JIM'S HOUSE to BANK:** Coordinates: JIM'S HOUSE $(6, 4)$, BANK $(-9, -3)$ $$d = \sqrt{(-9 - 6)^2 + (-3 - 4)^2} = \sqrt{(-15)^2 + (-7)^2} = \sqrt{225 + 49} = \sqrt{274}$$ $$d_{miles} = 0.75 \times \sqrt{274} \approx 0.75 \times 16.5529 = 12.41$$ miles **Final answers:** - Distance from GROCERY STORE to JIM'S HOUSE: approximately 11.15 miles - Distance from BANK to MALL: approximately 5.41 miles - Distance from JIM'S HOUSE to BANK: approximately 12.41 miles