Question

if you change the sign of a points y - coordinate from positive to negative, how will the location of the point change? the point will cross over the y - axis. the point will cross over the x - axis. the point will move up and to the right. not enough information is provided.

Explanation:

Step1: Recall coordinate system reflection rules

In a coordinate system \((x,y)\), changing the sign of the \(y\) - coordinate (i.e., \((x,y)\to(x, - y)\)) is a reflection over the \(x\) - axis.

Step2: Analyze each option

• For the option “The point will cross over the \(y\) - axis”: A reflection over the \(y\) - axis changes the \(x\) - coordinate sign (\((x,y)\to(-x,y)\)), so this option is wrong.
• For the option “The point will cross over the \(x\) - axis”: As \((x,y)\to(x, - y)\) is a reflection over the \(x\) - axis, this option is correct.
• For the option “The point will move up and to the right”: Changing the sign of the \(y\) - coordinate does not involve a translation (movement up/down or left/right in a non - reflective sense), so this option is wrong.
• For the option “Not enough information is provided”: We have the rule of coordinate transformation \((x,y)\to(x, - y)\) which is well - defined in the coordinate system, so this option is wrong.

Answer:

The point will cross over the \(x\) - axis.