Kamie is standing at K facing north. Kamie turns through an angle of $135^ ext{o}$ in an anti-clockwise direction, followed by $\frac{1}{4}$-turn in the clockwise direction. Which point will Kamie be facing?

1. Calculate the net angle of turn.

A $\frac{1}{4}$-turn is $90^\circ$.
Net turn $= 135^\circ \text{ anti-clockwise} - 90^\circ \text{ clockwise} = 45^\circ \text{ anti-clockwise}$.

2. Determine the final facing direction.

Turning $45^\circ$ anti-clockwise from North results in facing North-West.

3. Identify the point that lies North-West of K on the grid.

On a square grid, North-West corresponds to moving left and up by an equal number of units.
From K $(5, 4)$, moving $2$ units left and $2$ units up gives $(3, 6)$, which is the exact location of point C.