Question

rotate the shape by 180° counterclockwise.

Explanation:

Step1: Determine the rotation rule

When rotating a point \((x,y)\) by \(180^{\circ}\) counter - clockwise about the origin, the new coordinates \((x',y')\) are given by the rule \((x',y')=(-x,-y)\).

Step2: Identify the original points

Let's assume the three vertices of the triangle have coordinates. Suppose one vertex is \((- 6,-7)\), another is \((2,-7)\), and the third is \((2,1)\).

Step3: Apply the rotation rule

For the point \((-6,-7)\):
Using the formula \((x',y') = (-x,-y)\), we substitute \(x=-6\) and \(y = - 7\). Then \(x'=-(-6)=6\) and \(y'=-(-7) = 7\). So the new point is \((6,7)\).
For the point \((2,-7)\):
Substitute \(x = 2\) and \(y=-7\) into \((x',y')=(-x,-y)\). We get \(x'=-2\) and \(y' = 7\). So the new point is \((-2,7)\).
For the point \((2,1)\):
Substitute \(x = 2\) and \(y = 1\) into \((x',y')=(-x,-y)\). We get \(x'=-2\) and \(y'=-1\). So the new point is \((-2,-1)\).

Step4: Connect the new points

Plot the points \((6,7)\), \((-2,7)\) and \((-2,-1)\) on the coordinate plane and connect them to form the rotated triangle.

Answer:

The rotated triangle has vertices at \((6,7)\), \((-2,7)\) and \((-2,-1)\) (assuming the original vertices were \((-6,-7)\), \((2,-7)\) and \((2,1)\)).