Question

the graph shows triangles abc and abc. which sequence of transformations maps abc onto abc? a rotation 90° clockwise around the origin followed by a translation up 2 units a rotation 180° around the origin followed by a translation up 11 units a reflection across the y - axis followed by a translation up 4 units

Explanation:

Step1: Recall rotation and reflection rules

For a 90 - degree clockwise rotation around the origin, the transformation rule for a point $(x,y)$ is $(y, - x)$. For a 180 - degree rotation around the origin, the rule for a point $(x,y)$ is $(-x,-y)$. For a reflection across the y - axis, the rule for a point $(x,y)$ is $(-x,y)$. For a translation, we add or subtract values from the x and y coordinates.

Step2: Analyze the given triangles

Let's assume a general point on $\triangle ABC$ and see how it is transformed to $\triangle A'B'C'$. By observing the graph, we can see that if we first rotate $\triangle ABC$ 90 - degree clockwise around the origin and then translate it up 2 units, we can map $\triangle ABC$ onto $\triangle A'B'C'$.

Answer:

a rotation 90° clockwise around the origin followed by a translation up 2 units