Question

quadrilateral ( jklm ) is rotated ( -270^{circ} ) about the origin. draw the image of this rotation.

Explanation:

Step1: Recall the rotation rule

A rotation of \(-270^{\circ}\) about the origin is equivalent to a rotation of \(90^{\circ}\) clockwise. The rule for a \(90^{\circ}\) clockwise rotation about the origin is \((x,y)\to(y, -x)\).

Step2: Apply the rule to each vertex

Assume the coordinates of the vertices of quadrilateral \(JKLM\) are \(J(x_J,y_J)\), \(K(x_K,y_K)\), \(L(x_L,y_L)\), \(M(x_M,y_M)\). After rotation, the new coordinates will be \(J'(y_J,-x_J)\), \(K'(y_K,-x_K)\), \(L'(y_L,-x_L)\), \(M'(y_M,-x_M)\).

Step3: Plot the new vertices

Using the new coordinates from Step 2, plot each vertex \(J'\), \(K'\), \(L'\), \(M'\) on the coordinate plane and connect them to form the rotated quadrilateral.

Answer:

Follow the above steps to draw the rotated quadrilateral. First, determine the coordinates of the original vertices, then apply the \((x,y)\to(y, -x)\) rule, and finally plot and connect the new vertices.