Question

1 a graph of a geometric figure is below. which of the following graphs shows a rotation of 180° clockwise? a graph a b graph b c graph c d graph d

Explanation:

Step1: Recall 180° rotation rule

For a point \((x,y)\), a \(180^\circ\) clockwise (or counter - clockwise) rotation about the origin transforms it to \((-x,-y)\). We can identify key vertices of the original geometric figure from the graph and then apply this rule to find the corresponding vertices after rotation.

Step2: Analyze original figure's vertices

Let's assume the original figure has vertices (we can estimate from the grid). For example, if we take a vertex of the original figure, say \((x_1,y_1)\), after \(180^\circ\) rotation, it should be \((-x_1,-y_1)\).

Step3: Check each option

• Option A: The vertices do not follow the \((x,y)\to(-x,-y)\) transformation.
• Option B: The vertices do not match the \(180^\circ\) rotation transformation.
• Option C: By checking the vertices, we can see that each vertex \((x,y)\) of the original figure is transformed to \((-x,-y)\) in this graph, which is consistent with the \(180^\circ\) rotation rule.
• Option D: The vertices do not follow the \(180^\circ\) rotation transformation.

Answer:

C