Question

15 the following figure represents the rotation of \\( \triangle t u v \\) to \\( \triangle t ^ { prime } u ^ { prime } v ^ { prime } \\). find the degree of rotation in counter clockwise direction around the origin. answer: degree

Explanation:

Step1: Analyze the rotation of a point

Take a point (e.g., point \(T\)). Assume the original coordinates of \(T\) are \((x_1,y_1)\) and the rotated coordinates are \((x_2,y_2)\).

Step2: Use the property of rotation

When a point \((x,y)\) is rotated \(180^{\circ}\) counter - clockwise around the origin, the transformation rule is \((x,y)\to(-x, - y)\).
By observing the positions of corresponding points (e.g., \(T\) and \(T'\), \(U\) and \(U'\), \(V\) and \(V'\)) in the coordinate system, we can see that the \(x\) and \(y\) coordinates of each point of \(\triangle TUV\) change their signs to get the coordinates of the corresponding points of \(\triangle T'U'V'\).

Answer:

\(180\)