Question

question 1 of 10
abcd is rotated counterclockwise about the origin. by how many deg
was abcd rotated?

Explanation:

Step1: Analyze the rotation of a point

Take point \(A\) (assume coordinates \((2,1)\)) and its image \(A'\) (assume coordinates \((1, - 2)\)).

Step2: Use the rotation rule

For a counter - clockwise rotation of \(90^{\circ}\) about the origin, the transformation rule for a point \((x,y)\) is \((x,y)\to(-y,x)\). If we consider a rotation of \(180^{\circ}\), the rule is \((x,y)\to(-x,-y)\), and for \(270^{\circ}\) counter - clockwise \((x,y)\to(y, - x)\).
For a \(90^{\circ}\) counter - clockwise rotation, if we assume a general point \((x,y)\) in the original figure \(ABCD\), after rotation, its image \((x',y')\) satisfies \(x'=-y\) and \(y' = x\). By checking the relative positions of multiple points (e.g., \(B\) and \(B'\), \(C\) and \(C'\), \(D\) and \(D'\)) in the coordinate - plane, we can confirm that the rotation angle is \(90^{\circ}\).

Answer:

A. \(90^{\circ}\)