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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To find the total distance traveled, we need to calculate the distance between each pair of points and then add them up.
First, let's find the distance between the sledding and ice skating locations:
Distance = $\sqrt{ (2 - 2)^2 + (12 - (-4))^2} = \sqrt{0 + 16^2} = \sqrt{256} = 16$
Next, let's find the distance between the ice skating and skiing locations:
Distance = $\sqrt{ (2 - (-8))^2 + (-4 - (-4))^2} = \sqrt{10^2 + 0} = \sqrt{100} = 10$
Finally, let's find the distance between the sledding and skiing locations:
Distance = $\sqrt{ (2 - (-8))^2 + (12 - (-4))^2} = \sqrt{10^2 + 16^2} = \sqrt{100 + 256} = \sqrt{356} \approx 18.87$
Now let's add up the distances:
$16 + 10 + 18.87 \approx 44.87$
Therefore, the total distance traveled between these locations is approximately 44.87.