Question

which are the new coordinates of point ( a(2,3) ) after performing a reflection of ( \triangle abc ) across the ( y )-axis followed by a ( 90^{circ} ) counterclockwise rotation about the origin?
( (-3,2) )
( (3,-2) )
( (-2,-3) )
( (-3,-2) )

Explanation:

Step1: Reflection across the y - axis

The rule for reflection across the y - axis is \((x,y)\to(-x,y)\).
For the point \(A(2,3)\), after reflection across the y - axis, the new point is \((- 2,3)\).

Step2: \(90^{\circ}\) counter - clockwise rotation about the origin

The rule for a \(90^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(-y,x)\).
For the point \((-2,3)\), after rotation, we substitute \(x=-2\) and \(y = 3\) into the rule: \((-3,-2)\)

Answer:

\((-3,-2)\)