Question

△elm is rotated - 90° about the origin. draw the image of this rotation.

Explanation:

Step1: Determine the rotation rule

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

Step2: Find the coordinates of points \(L\), \(M\), and \(E\)

• Point \(L\) has coordinates \((3,2)\).
• Point \(M\) has coordinates \((6,7)\).
• Point \(E\) has coordinates \((7,-3)\).

Step3: Apply the rotation rule to each point

• For \(L(3,2)\): Using the rule \((x,y)\to(y, -x)\), we get \(L'(2,-3)\).
• For \(M(6,7)\): Using the rule \((x,y)\to(y, -x)\), we get \(M'(7,-6)\).
• For \(E(7,-3)\): Using the rule \((x,y)\to(y, -x)\), we get \(E'(-3,-7)\).

Step4: Plot the new points and draw the triangle

Plot \(L'(2,-3)\), \(M'(7,-6)\), and \(E'(-3,-7)\) on the coordinate plane and connect them to form the rotated triangle \(\triangle E'L'M'\).

Answer:

Plot the points \(L'(2,-3)\), \(M'(7,-6)\), and \(E'(-3,-7)\) and connect them to draw the image of \(\triangle ELM\) after a \(-90^{\circ}\) rotation about the origin.