Question

triangle pqr is shown on the set of axes below. which quadrant will contain point r, the image of point r, after a 90° clockwise rotation centered at (0,0) followed by a reflection over the x - axis? 1) i 2) ii 3) iii 4) iv

Explanation:

Step1: Determine the quadrant of point \( R \)

Assume \( R=(x,y) \) where \( x>0,y>0 \) (since it is in the first - quadrant).
The rule for a \( 90^{\circ} \) clockwise rotation about the origin \((0,0)\) is \((a,b)\to(b, - a)\). So, if \( R=(x,y) \), after a \( 90^{\circ} \) clockwise rotation about the origin, \( R'=(y,-x) \).

Step2: Apply the reflection over the \( x \) - axis

The rule for a reflection over the \( x \) - axis is \((m,n)\to(m, - n)\).
If \( R'=(y,-x) \), after reflection over the \( x \) - axis, \( R''=(y,x) \)

Answer:

1. I