Question

in which quadrant will the image of figure pqrs be located after a reflection across the x - axis? quadrant i quadrant ii quadrant iii quadrant iv

Explanation:

Step1: Recall the rule for reflection across the x - axis

When a point \((x,y)\) is reflected across the \(x\) - axis, the new point is \((x,-y)\).

Step2: Determine the original quadrant of figure \(PQRS\)

From the graph, figure \(PQRS\) is in Quadrant II (where \(x<0\) and \(y > 0\)).

Step3: Apply the reflection rule

After reflection across the \(x\) - axis, for each point \((x,y)\) in \(PQRS\) (with \(x<0,y>0\)), the new points will be \((x,-y)\) (where \(x < 0\) and \(-y<0\)).

Step4: Identify the quadrant of the reflected figure

Points with \(x<0\) and \(y < 0\) lie in Quadrant III.

Answer:

Quadrant III