Question

using the coordinate plane, which of the following statements would result in figure abcd being in quadrant iv? figure abcd is translated 4 units to the left and 2 units down. figure abcd is reflected across the x - axis. figure abcd is rotated 90° about point b. figure abcd is reflected across the y - axis. question 13 1 pts a triangle is in the first quadrant of an x - y coordinate system, as shown here:

Explanation:

Step1: Analyze Quadrant IV properties

Quadrant IV has positive \(x\)-coordinates and negative \(y\)-coordinates. Original figure \(ABCD\) is in Quadrant I (positive \(x\), positive \(y\)).

Step2: Evaluate each option

• Option 1 (Translate 4 left, 2 down): Left translation decreases \(x\), down decreases \(y\). Could move to Quadrant II or III (if \(x\) becomes negative), not IV.
• Option 2 (Reflect across \(x\)-axis): Reflecting over \(x\)-axis changes \(y\)-sign (positive to negative) while \(x\) remains positive. So new coordinates: positive \(x\), negative \(y\) → Quadrant IV.
• Option 3 (Rotate \(90^\circ\) about \(B\)): Rotation about a point in Quadrant I will likely keep it in Quadrant I or move to II/III, not IV.
• Option 4 (Reflect across \(y\)-axis): Reflecting over \(y\)-axis changes \(x\)-sign (positive to negative), so negative \(x\), positive \(y\) → Quadrant II.

Answer:

The correct option is: Figure \(ABCD\) is reflected across the \(x\)-axis.