Question

2 describe a sequence of transformations that maps △pqr onto △lmn.

Explanation:

Step1: Analyze orientation change

Notice that $\triangle PQR$ and $\triangle LMN$ have different orientations. First, reflect $\triangle PQR$ over the x - axis. Let the coordinates of the vertices of $\triangle PQR$ be $P(x_1,y_1)$, $Q(x_2,y_2)$, $R(x_3,y_3)$. After reflection over the x - axis, the new coordinates are $P'(x_1, - y_1)$, $Q'(x_2,-y_2)$, $R'(x_3,-y_3)$.

Step2: Analyze position change

After reflection, we need to translate the reflected triangle to match $\triangle LMN$. Count the number of units of horizontal and vertical translation. We can see that we need to translate the reflected triangle 3 units to the right and 1 unit down. If a point has coordinates $(x,y)$ after reflection, after translation 3 units to the right and 1 unit down, the new coordinates are $(x + 3,y-1)$.

Answer:

First, reflect $\triangle PQR$ over the x - axis, then translate the reflected triangle 3 units to the right and 1 unit down.