Describing Rotations

Let's first draw $\triangle JKL$ by plotting vertices $J(2,6),$ $K(5,2),$ and $L(7,5).$

To rotate the figure $90^\circ$ counterclockwise about the origin, we can focus on its vertices.

We will begin by rotating vertex $J.$ To do so, we will first draw a segment from $J$ to the origin. Then, we will draw another segment from the origin to the image of $J$ such that both segments are congruent and perpendicular.

Similarly, we will rotate the other vertices to have $\triangle J'K'L'.$

By connecting the rotated points, we can finally have the image of $\triangle JKL.$