Question

1b) describe a sequence of transformations that maps △abc onto △def (first transformation) followed by (second transformation)

Explanation:

Step1: Analyze horizontal and vertical shift

Count the grid - squares. To move $\triangle ABC$ to a position similar to $\triangle DEF$ in terms of orientation and relative position on the grid, first, translate $\triangle ABC$ 5 units to the left and 3 units down. Let the coordinates of the vertices of $\triangle ABC$ be $(x,y)$. After translation, the new coordinates $(x',y')$ are given by $x'=x - 5$ and $y'=y-3$.

Step2: Analyze rotation

After the translation, rotate the translated triangle $180^{\circ}$ about the origin. The rule for a $180^{\circ}$ rotation about the origin for a point $(x,y)$ is $(x,y)\to(-x,-y)$.

Answer:

First transformation: Translation 5 units left and 3 units down. Second transformation: Rotation of $180^{\circ}$ about the origin.