Determine if the following statement makes sense:After plotting the point with rectangular coordinates (0,−4), a student found polar coordinates without having to show any work.Group of answer choicesThe statement does not make sense because the point (0,−4) is already in the form of the polar coordinates.The statement does not make sense because it is not possible to find the polar coordinates without using the formula for the polar representation.The statement does make sense because the point (0,−4) is represented the same way in polar coordinates.The statement does make sense because the coordinate of the rectangular 𝑥−coordinates is 0.
Question
Determine if the following statement makes sense:After plotting the point with rectangular coordinates (0,−4), a student found polar coordinates without having to show any work.Group of answer choicesThe statement does not make sense because the point (0,−4) is already in the form of the polar coordinates.The statement does not make sense because it is not possible to find the polar coordinates without using the formula for the polar representation.The statement does make sense because the point (0,−4) is represented the same way in polar coordinates.The statement does make sense because the coordinate of the rectangular 𝑥−coordinates is 0.
Solution
The statement does not make sense because it is not possible to find the polar coordinates without using the formula for the polar representation.
To convert from rectangular coordinates (x, y) to polar coordinates (r, θ), we use the formulas r = √(x² + y²) and θ = atan(y/x). In this case, for the point (0, -4), r = √(0² + (-4)²) = 4 and θ = atan(-4/0), but atan is undefined for 0. Therefore, some calculations are needed to find the polar coordinates, so it doesn't make sense to say that a student found the polar coordinates without showing any work.
Similar Questions
Determine if the following statement makes sense:The student must have made a mistake because the student’s polar representation of a given point has a different answer than the back of the book.Group of answer choicesThe statement does not make sense because there is a possibility that the student used the wrong formula.The statement does make sense because the polar representations should be the same for the same point.The statement does not make sense because the polar representations can be different for the same point.The statement does make sense because the student made the wrong interpretation for the formula of polar representation.
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