Question

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

Explanation:

Step1: Recall the property of points with same \(y\) - coordinate and opposite \(x\) - coordinate

If two points have coordinates \((x,y)\) and \((-x,y)\), they are symmetric about the \(y\) - axis.

Step2: Analyze each graph

• For the first graph: If we assume one point is \((x,y)\) and the other is \((-x,y)\) (same \(y\) - value, \(x\) and \(-x\) as \(x\) - values), it satisfies the condition.
• For the second graph: The \(y\) - values of the two points are different.
• For the third graph: The \(y\) - values of the two points are different.
• For the fourth graph: The \(y\) - values of the two points are different.

Answer:

The first graph (the one with two points at the same height above the \(x\) - axis and symmetric about the \(y\) - axis) is the correct graph.