Question

7
multiple choice 1 point
determine if the graph below has point symmetry, line symmetry, or no symmetry.
no symmetry
line symmetry
point symmetry

Explanation:

• Line symmetry: A graph has line symmetry if there is a line (e.g., \(y = x\), \(x = 0\), \(y=0\)) such that when the graph is folded along that line, the two halves match exactly. For a graph to have line symmetry about the \(y\) - axis (\(x = 0\)), if \((x,y)\) is on the graph, then \((-x,y)\) is on the graph. For line symmetry about the \(x\) - axis (\(y = 0\)), if \((x,y)\) is on the graph, then \((x, - y)\) is on the graph.
• Point symmetry: A graph has point symmetry about the origin \((0,0)\) if for every point \((x,y)\) on the graph, the point \((-x,-y)\) is also on the graph.
• Looking at the given graph, we can check for line symmetry. If we assume a vertical line \(x = a\) (the most common candidate for line - symmetry in a Cartesian plane for non - rotated graphs is \(x = 0\)). If we take a point \((x,y)\) on the left - hand side of the \(y\) - axis, there is no corresponding point \((-x,y)\) on the right - hand side of the \(y\) - axis such that the distances from the \(y\) - axis are equal and the \(y\) - values are the same.
• For point symmetry, if we take a point \((x,y)\) on the graph, there is no point \((-x,-y)\) on the graph.
• Since there is no line or point about which the graph can be symmetrically mapped onto itself.

Answer:

no symmetry