The total distance Lisa traveled on her bicycle is 16.50 miles
Explanation:
The formula for distance between points given coordinates is given by;
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
where (x, y) represents coordinates of a point.
Finding the distance from home (5,2) to school (4,-3)
Applying the distance formula where x₁=5,x₂=4, y₁=2, y₂=-3
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\\\d=\sqrt{(4-5)^2+(-3-2)^2} \\\\\\d=\sqrt{(-1^2)+(-5^2)} \\\\d=\sqrt{1+25} =\sqrt{26} =5.099](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5Cd%3D%5Csqrt%7B%284-5%29%5E2%2B%28-3-2%29%5E2%7D%20%5C%5C%5C%5C%5C%5Cd%3D%5Csqrt%7B%28-1%5E2%29%2B%28-5%5E2%29%7D%20%5C%5C%5C%5Cd%3D%5Csqrt%7B1%2B25%7D%20%3D%5Csqrt%7B26%7D%20%3D5.099)
Finding distance from school (4,-3) to library (0,2)
Here x₁=4,x₂=0,y₁= -3 ,y₂=2
![d=\sqrt{(0-4)^2+(2--3)^2} \\\\\\d=\sqrt{-4^2+5^2} \\\\d=\sqrt{16+25} =\sqrt{41} =6.403](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%280-4%29%5E2%2B%282--3%29%5E2%7D%20%5C%5C%5C%5C%5C%5Cd%3D%5Csqrt%7B-4%5E2%2B5%5E2%7D%20%5C%5C%5C%5Cd%3D%5Csqrt%7B16%2B25%7D%20%3D%5Csqrt%7B41%7D%20%3D6.403)
Finding the distance from the library (0,2) to home(5,2) where x₁=0,x₂=5,y₁=2,y₂=2
![d=\sqrt{(5-0)^2+(2-2)^2} \\\\\\d=\sqrt{5^2} =\sqrt{25} =5](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%285-0%29%5E2%2B%282-2%29%5E2%7D%20%5C%5C%5C%5C%5C%5Cd%3D%5Csqrt%7B5%5E2%7D%20%3D%5Csqrt%7B25%7D%20%3D5)
Total distance traveled is: 5.099 + 6.403+5.0 =16.50 miles
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Distance between points :brainly.com/question/11213233
Keywords : coordinates, location, distance
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