Question

draw a complete graph so that it has symmetry with respect to the origin.
choose the correct graph.

Explanation:

Step1: Recall the property of symmetry about the origin

A graph is symmetric about the origin if for every point \((x,y)\) on the graph, the point \((-x,-y)\) is also on the graph.

Step2: Analyze each option

• Option A: Does not satisfy the condition \((-x,-y)\) for all points \((x,y)\) on the graph.
• Option B: Does not satisfy the condition \((-x,-y)\) for all points \((x,y)\) on the graph.
• Option C: Does not satisfy the condition \((-x,-y)\) for all points \((x,y)\) on the graph.
• Option D: For every point \((x,y)\) on the graph, the point \((-x,-y)\) is also on the graph.

Answer:

D.