Question

which blue triangle shows a 90° counterclockwise rotation of the green triangle? choose three correct answers

Explanation:

Step1: Understand the rule of 90° counter - clockwise rotation

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise about the origin \((0,0)\), the transformation rule is \((x,y)\to(-y,x)\). For a right - angled triangle (assuming the right - angle vertex is at a certain point), we can check the position of the vertices.
Let's assume the right - angle vertex of the green triangle is at \((a,b)\). After a \(90^{\circ}\) counter - clockwise rotation, its new position should be \((-b,a)\).

Step2: Analyze each option

• For the first option (top - left):

If we consider the orientation of the right - angle and the relative position of the vertices with respect to the origin, we can see that it does not follow the \(90^{\circ}\) counter - clockwise rotation rule.

• For the second option (top - right):

By checking the position of the vertices (especially the right - angle vertex) with respect to the origin, we find that it follows the \(90^{\circ}\) counter - clockwise rotation rule.

• For the third option (middle - left):

It does not follow the \(90^{\circ}\) counter - clockwise rotation rule as the orientation and vertex positions are not in line with the transformation \((x,y)\to(-y,x)\).

• For the fourth option (middle - right):

It follows the \(90^{\circ}\) counter - clockwise rotation rule. The right - angle vertex and the other vertices are re - positioned according to the \((x,y)\to(-y,x)\) transformation.

• For the fifth option (bottom):

It follows the \(90^{\circ}\) counter - clockwise rotation rule. The relative position of the vertices (including the right - angle vertex) with respect to the origin is consistent with the \((x,y)\to(-y,x)\) transformation.

Answer:

The second (top - right), fourth (middle - right), and fifth (bottom) options are correct.