Question

determine the type of rotation below *
270 counterclockwise
270 clockwise
90 counterclockwise
180
90 clockwise
this is a required question

Explanation:

Step1: Recall rotation rules

For a point \((x,y)\) rotated \(90^{\circ}\) clockwise about the origin, the new coordinates are \((y, -x)\); for \(90^{\circ}\) counter - clockwise, \((-y,x)\); for \(180^{\circ}\), \((-x,-y)\); for \(270^{\circ}\) clockwise (equivalent to \(90^{\circ}\) counter - clockwise), \((-y,x)\); for \(270^{\circ}\) counter - clockwise (equivalent to \(90^{\circ}\) clockwise), \((y, -x)\).

Step2: Analyze the transformation

Let's assume a general point in the original triangle (black) and its corresponding point in the rotated triangle (blue). If we consider the direction of rotation. The rotation from the black triangle to the blue triangle is in the clockwise direction.
If we use the property of rotation matrices or the "hand - rule" (right - hand for clockwise, left - hand for counter - clockwise in a 2D plane with the standard coordinate system \(x\) - axis to the right and \(y\) - axis up). A \(270^{\circ}\) clockwise rotation is equivalent to a \(90^{\circ}\) counter - clockwise rotation. But if we track the orientation of the triangle:
Take a vertex, say if we consider the movement of the vertices of the triangle. A \(270^{\circ}\) clockwise rotation of a figure about the origin will move each point \((x,y)\) of the figure to \((y, -x)\) (by successive \(90^{\circ}\) clockwise rotations: one \(90^{\circ}\) clockwise \((x,y)\to(y, -x)\), two \(90^{\circ}\) clockwise \((x,y)\to(-x, -y)\), three \(90^{\circ}\) clockwise \((x,y)\to(-y,x)\)).

Answer:

270 clockwise