Question

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

Explanation:

Step1: Understand the coordinate property

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

Step2: Analyze the symmetry

These two points are symmetric about the \(x -\)axis.

Step3: Check each graph

• In the first graph (top - left), the points are symmetric about the \(y -\)axis (if \(x\) values are opposite and \(y\) values are the same).
• In the second graph (top - right), \(x\) values are not the same.
• In the third graph (bottom - left), for a given \(x\) value (non - zero), the \(y\) values are opposite. For example, if one point is \((a,b)\) and the other is \((a,-b)\).
• In the fourth graph (bottom - right), \(x\) values are not the same.

Answer:

The third graph (bottom - left) is the possible graph of these points.