Question

two points have the same y - coordinate but opposite x - coordinates. which is a possible graph of these points?

Explanation:

Step1: Analyze the property of points

If two points have the same \(y -\)coordinate but opposite \(x -\)coordinates, say the points are \((x,y)\) and \((-x,y)\).

Step2: Check the symmetry

In a coordinate plane, the points \((x,y)\) and \((-x,y)\) are symmetric about the \(y -\)axis.
Looking at the graphs:

• In the first graph (top - left), the points do not have the same \(y -\)coordinate.
• In the second graph (top - right), the points do not have the same \(y -\)coordinate.
• In the third graph (bottom - left), if we assume one point is \((x,y)\) and the other is \((-x,y)\), they are symmetric about the \(y -\)axis (same \(y -\)coordinate and opposite \(x -\)coordinates).
• In the fourth graph (bottom - right), the points do not have the same \(y -\)coordinate.

Answer:

The third graph (the one where the two points are symmetric about the \(y -\)axis) is the correct graph.