Questions: The figure on the coordinate plane is rotated 180° counterclockwise. Draw the resulting image of the figure on the coordinate grid.

Solution Steps

The vertices of the original figure are: \(A = (1, 1)\) \(B = (2, 4)\) \(C = (4, 3)\) \(D = (3, 1)\)

The rule for a 180° counterclockwise rotation is \((x, y) \rightarrow (-x, -y)\). Applying this rule to each vertex: \(A' = (-1, -1)\) \(B' = (-2, -4)\) \(C' = (-4, -3)\) \(D' = (-3, -1)\)

Plot the new vertices \(A', B', C', D'\) on the coordinate plane. Connect the vertices to form the rotated figure.

Final Answer

 5 |        .C
 4 |       .    .B
 3 |      .       .
 2 |     .         .
 1 |    .           .
 0 |___.___.___.___.___
   -1  0   1   2   3  4  5
-1 |  A' .
-2 |      .
-3 |        . D'
-4 |           . B'
-5 |              .C'