Question

2. Lisa rode her bicycle from her home to school, and then to the local library, before
finally returning home. The coordinates (5,2) represent the location of her home, the
coordinates (4, -3) represent the location of her school, and the coordinates (0,2)
represent the location of the library. If each unit represents 1 mile, which best
represents the total distance Lisa traveled on her bicycle?

Answer 1

The total distance Lisa traveled on her bicycle is 16.50 miles

Explanation:

The formula for distance between points given coordinates is given by;

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\\\d=\sqrt{(4-5)^2+(-3-2)^2} \\\\\\d=\sqrt{(-1^2)+(-5^2)} \\\\d=\sqrt{1+25} =\sqrt{26} =5.099$

Finding distance from school (4,-3) to library (0,2)

Here x₁=4,x₂=0,y₁= -3 ,y₂=2

$d=\sqrt{(0-4)^2+(2--3)^2} \\\\\\d=\sqrt{-4^2+5^2} \\\\d=\sqrt{16+25} =\sqrt{41} =6.403$

Finding the distance from the library (0,2) to home(5,2) where x₁=0,x₂=5,y₁=2,y₂=2

$d=\sqrt{(5-0)^2+(2-2)^2} \\\\\\d=\sqrt{5^2} =\sqrt{25} =5$

Total distance traveled is: 5.099 + 6.403+5.0 =16.50 miles

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Distance between points :https://brainly.com/question/11213233

Keywords : coordinates, location, distance

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