Question

△top is rotated - 180° about the origin. draw the image of this rotation.

Explanation:

Step1: Determine the rotation rule

The rule for a rotation of \(- 180^{\circ}\) (which is the same as a rotation of \(180^{\circ}\)) about the origin is \((x,y)\to(-x,-y)\).

Step2: Find the coordinates of the vertices

Assume the coordinates of \(T\) is \((6,0)\), \(O\) is \((-2,-5)\) and \(P\) is \((-2,5)\).
For point \(T(6,0)\):
Using the rule \((x,y)\to(-x,-y)\), we get \(T'(-6,0)\).
For point \(O(-2,-5)\):
Using the rule \((x,y)\to(-x,-y)\), we get \(O'(2,5)\).
For point \(P(-2,5)\):
Using the rule \((x,y)\to(-x,-y)\), we get \(P'(2,-5)\).

Step3: Plot the new triangle

Plot the points \(T'(-6,0)\), \(O'(2,5)\) and \(P'(2,-5)\) on the coordinate plane and connect them to form the rotated triangle \(\triangle T'O'P'\).

Answer:

Plot the points \(T'(-6,0)\), \(O'(2,5)\) and \(P'(2,-5)\) on the coordinate plane and connect them.