Based on the given scenario above, the coordinates of point Q is known to be (-3, 5).
What is the points about?
Note that if a point P(x, y) is rotated 90° counterclockwise around the origin, one has to flip x and y and reverse the sign of y.
So, The rule to rotate a point P(x, y) after a rotation 90° counterclockwise around the origin is said to be:
P(x, y) = P'(-y, x)
In this question, rectangle PQRS is rotated 90° counterclockwise about the origin.
The rectangle is said to have the coordinates:
P(2, 3)
Q(5, 3)
R(5, 1)
S(2, 1)
Therefore we look for the coordinates of the point Q’.
By using the rule to rotate a point P(x, y) after a rotation 90° counterclockwise around the origin, then:
P(x, y) = P'(-y, x)
Therefore, coordinates of the point Q’ will be:
Q(5, 3) = Q'(-3, 5)
Therefore, the coordinates of point Q' is: Q'(-3, 5)
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