Question

which are the new coordinates of point ( b(4,2) ) after performing a rotation of ( 90^{circ} ) clockwise about the origin followed by a reflection across the line ( y = x )?
( (2,4) )
( (-4,2) )
( (-2,-4) )
( (-4,-2) )

Explanation:

Step1: Rotate point \((4,2)\) \(90^{\circ}\) clockwise about the origin

When we rotate a point \((x,y)\) \(90^{\circ}\) clockwise about the origin, the transformation rule is \((x,y)\to(y, -x)\).
For the point \(B(4,2)\), after rotation, we get \((2,-4)\).

Step2: Reflect the rotated point across the line \(y = x\)

When we reflect a point \((x,y)\) across the line \(y=x\), the transformation rule is \((x,y)\to(y,x)\).
For the point \((2,-4)\), after reflection, we get \((-4,2)\).

Answer:

\((-4,2)\) (the second option)