Question

1. after a shape is translated 3 units up and then reflected across the x - axis, which quadrant will it end in if it started in quadrant i? quadrant i quadrant iv quadrant ii quadrant iii

Explanation:

Step1: Understand the effect of translation

Translation 3 units up does not change the quadrant in terms of left - right (x - coordinate sign). It only changes the y - coordinate. If a point \((x,y)\) is in Quadrant I (\(x>0,y > 0\)), after translation 3 units up, the new point is \((x,y + 3)\) and still \(x>0,y+3>0\).

Step2: Understand the effect of reflection across the x - axis

The rule for reflection across the x - axis is \((x,y)\to(x,-y)\). After reflection across the x - axis, if the original point after translation was \((x,y + 3)\) (\(x>0,y+3>0\)), the new point is \((x,-(y + 3))\). Since \(x>0\) and \(-(y + 3)<0\)

Answer:

Quadrant IV