Question

copy each diagram and rotate the shape about the centre c by the given number of degrees.

Explanation:

Step1: Recall rotation rules

For a rotation about a center point \(C\), each point of the shape moves around \(C\) by the given angle.

Step2: Rotate shape a

For shape a, if rotating say \(90^{\circ}\) counter - clockwise about \(C\), we take each vertex of the triangle and move it \(90^{\circ}\) counter - clockwise around \(C\). We use the property that for a \(90^{\circ}\) counter - clockwise rotation of a point \((x,y)\) about the origin (similarly for a center \(C\)) the new coordinates \((x',y')\) are \((-y,x)\) after appropriate translation to make \(C\) the origin and then back - translation.

Step3: Rotate shape b

For shape b, if rotating \(180^{\circ}\) about \(C\), a point \((x,y)\) relative to \(C\) becomes \((-x,-y)\). We apply this rule to each vertex of the L - shaped figure.

Step4: Rotate shape c

For shape c, say rotating \(270^{\circ}\) counter - clockwise (or \(90^{\circ}\) clockwise) about \(C\). Using rotation transformation rules for points around \(C\), we find the new positions of the vertices of the trapezoid - like shape.

Step5: Rotate shape d

For shape d, if rotating \(360^{\circ}\) about \(C\), the shape remains in the same position as a \(360^{\circ}\) rotation is a full turn and brings the shape back to its original orientation.

Answer:

The rotated shapes are obtained by applying the above - mentioned rotation rules for each of the given shapes about the center \(C\) with the given angles of rotation. The actual drawing of the rotated shapes would require using a protractor and ruler to accurately plot the new positions of the vertices on the grid paper.