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 rotation of \(270^{\circ}\) clockwise) about the origin is \((x,y)\to(y, -x)\).

Step2: Find the coordinates of the original points

Assume the coordinates of the vertices of \(\triangle ELM\) are: Let's say \(E(6,-3)\), \(L(3,2)\), \(M(6,7)\)

Step3: Apply the rotation rule

For point \(E(6,-3)\):
Using the rule \((x,y)\to(y, -x)\), we substitute \(x = 6\) and \(y=-3\).
The new coordinates are \((-3,-6)\)
For point \(L(3,2)\):
Substitute \(x = 3\) and \(y = 2\) into the rule \((x,y)\to(y,-x)\)
The new coordinates are \((2,-3)\)
For point \(M(6,7)\):
Substitute \(x = 6\) and \(y = 7\) into the rule \((x,y)\to(y,-x)\)
The new coordinates are \((7,-6)\)

Step4: Plot the new points

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

Answer:

To draw the image of the rotation:

1. Locate the new points \((-3,-6)\) (image of \(E\)), \((2,-3)\) (image of \(L\)) and \((7,-6)\) (image of \(M\)) on the coordinate grid.
2. Connect these three new points to form the rotated triangle \(\triangle E'L'M'\) (where \(E'\), \(L'\), \(M'\) are the rotated vertices).