Calculus III: Three Dimensional Coordinate Systems (Level 4 of 10)

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Mathematics
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9th - 10th Grade
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Hard
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main difference when extending the midpoint formula from 2D to 3D?
Adding a new variable for time
Including the z-coordinate
Using polar coordinates
Changing the formula completely
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example provided, what are the coordinates of the midpoint between (4,3,1) and (-2,5,7)?
(2, 4, 5)
(1, 4, 4)
(3, 4, 4)
(1, 5, 4)
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the geometric significance of the midpoint in a line segment?
It divides the line into two equal parts
It is the endpoint of the line
It divides the line into two unequal parts
It is the starting point of the line
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What mathematical theorem is used to derive the distance formula in both 2D and 3D?
Binomial Theorem
Pythagorean Theorem
Fundamental Theorem of Calculus
Fermat's Last Theorem
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How many times is the Pythagorean theorem applied to derive the 3D distance formula?
Four times
Three times
Twice
Once
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of right triangles in deriving the 3D distance formula?
They are not used at all
They are used to relate the lengths of line segments
They help in visualizing the coordinate system
They are used to calculate angles
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which coordinate differences are used to find the length of the blue line segment in the derivation?
x and y coordinates
y and z coordinates
x and z coordinates
Only x coordinates
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