Question

point p is located at (-4, -7). p is reflected across the x-axis to create p. in which quadrant is p located?
○ quadrant i
○ quadrant ii
○ quadrant iii
○ quadrant iv

Explanation:

Step1: Recall reflection over x - axis rule

When a point \((x,y)\) is reflected across the \(x\) - axis, the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. So the rule for reflection over the \(x\) - axis is \((x,y)\to(x, - y)\).

Step2: Apply the rule to point \(P(-4,-7)\)

For point \(P(-4,-7)\), using the reflection rule over the \(x\) - axis, the \(x\) - coordinate \(x=-4\) remains the same, and the \(y\) - coordinate \(y = - 7\) changes to \(-y=7\). So the coordinates of \(P'\) are \((-4,7)\).

Step3: Determine the quadrant of \(P'(-4,7)\)

In the coordinate plane, Quadrant II is defined as the set of points where the \(x\) - coordinate is negative and the \(y\) - coordinate is positive (\(x<0,y > 0\)). For the point \(P'(-4,7)\), \(x=-4<0\) and \(y = 7>0\), so it lies in Quadrant II.

Answer:

B. Quadrant II