Question

question 11
1 pts
image of coordinate plane with figure abcd
using the coordinate plane, which of the following statements would result in figure abcd being in quadrant ii?

• figure abcd is reflected across the x-axis.
• figure abcd is rotated 90° about point b.
• figure abcd is translated 4 units to the left and 2 units down.
• figure abcd is reflected across the y-axis.

Explanation:

Step1: Analyze Quadrant II properties

Quadrant II has \( x < 0 \) and \( y>0 \). Original figure \( ABCD \) is in Quadrant I (\( x > 0,y > 0 \)).

Step2: Evaluate each option

• Reflect across \( x \)-axis: \((x,y)\to(x, - y)\), moves to Quadrant IV (\( x>0,y < 0 \)) – incorrect.
• Rotate \( 90^\circ \) about \( B \): Unlikely to move to Quadrant II (depends on rotation direction, but not a standard reflection/translation to Quadrant II) – incorrect.
• Translate 4 left, 2 down: New coordinates \((x - 4,y - 2)\). Original \( x>0 \), \( x - 4 \) may be positive or negative, \( y-2\) may be positive or negative – not guaranteed Quadrant II – incorrect.
• Reflect across \( y \)-axis: \((x,y)\to(-x,y)\). Now \( x < 0,y > 0 \), which is Quadrant II – correct.

Answer:

Figure \( ABCD \) is reflected across the \( y \)-axis.