The new coordinate is (7,-9) when the coordinate axes is rotated 45° counterclockwise. What is the old coordinate?Question 5AnswerA.(-1.41, -13.31)B.(-1.21, -11.31)C.(-1.31, -11.31)D.(-1.41, -11.31)
Question
The new coordinate is (7,-9) when the coordinate axes is rotated 45° counterclockwise. What is the old coordinate?Question 5AnswerA.(-1.41, -13.31)B.(-1.21, -11.31)C.(-1.31, -11.31)D.(-1.41, -11.31)
Solution
To find the old coordinates, we need to rotate the new coordinates 45° clockwise (which is the opposite of counterclockwise).
The formula for rotating a point (x, y) around the origin by an angle θ (in this case, 45° or π/4 radians) clockwise is given by:
x' = xcosθ + ysinθ y' = -xsinθ + ycosθ
Substituting the given values (x = 7, y = -9, θ = -π/4) into the formula, we get:
x' = 7cos(-π/4) - 9sin(-π/4) = 7/sqrt(2) + 9/sqrt(2) = 16/sqrt(2) = 11.31 (approx) y' = -7sin(-π/4) - 9cos(-π/4) = 7/sqrt(2) - 9/sqrt(2) = -2/sqrt(2) = -1.41 (approx)
So, the old coordinates are approximately (-1.41, -11.31), which corresponds to option D.
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