The Coordinate Plane Unit Test
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Question
Use the image to answer the question.
A coordinate grid shows the x-axis ranging from negative 12 to 12 and the y-axis also ranging from negative 12 to 12. Points labeled with winter activities are plotted. Sledding is plotted at left parenthesis 2 comma 12 right parenthesis. Skiing is plotted at left parenthesis negative 8 comma negative 4 right parenthesis, and ice skating is plotted at left parenthesis 2 comma negative 4 right parenthesis.
Shahriyar is at a winter park with his family. They go sledding first, then ice skating, then skiing. What is the total distance traveled between these locations?
(1 point)
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The total distance traveled between these locations can be found by adding up the distances between each pair of points.
First, we find the distance between the point for sledding (2, 12) and the point for ice skating (2, -4):
Distance = sqrt((2 - 2)^2 + (-4 - 12)^2) = sqrt(0 + 256) = sqrt(256) = 16
Next, we find the distance between the point for ice skating (2, -4) and the point for skiing (-8, -4):
Distance = sqrt((-8 - 2)^2 + (-4 - -4)^2) = sqrt((-10)^2 + 0^2) = sqrt(100) = 10
Finally, we find the distance between the point for sledding (2, 12) and the point for skiing (-8, -4):
Distance = sqrt((-8 - 2)^2 + (-4 - 12)^2) = sqrt((-10)^2 + (-16)^2) = sqrt(100 + 256) = sqrt(356) ≈ 18.89
The total distance traveled is 16 + 10 + 18.89 = 44.89.
Therefore, the total distance traveled between these locations is approximately 44.89.