Question

the graph shows triangles rst and rst.
which of the following transformations maps rst onto rst?
translation up 8 units
translation up 12 units
reflection across the x-axis
reflection across the y-axis
rotation $90^{\circ}$ clockwise around the origin
rotation $90^{\circ}$ counterclockwise around the origin
rotation $180^{\circ}$ around the origin

Explanation:

Step1: Identify coordinates of R

Original $R: (-1, -6)$; Image $R': (-1, 6)$

Step2: Identify coordinates of S

Original $S: (-3, -3)$; Image $S': (-3, 3)$

Step3: Identify coordinates of T

Original $T: (6, -4)$; Image $T': (6, 4)$

Step4: Check transformation rule

For a point $(x,y)$, reflection over x-axis is $(x,-y)$.
For $R(-1,-6)$: $(-1, -(-6))=(-1,6)=R'$
For $S(-3,-3)$: $(-3, -(-3))=(-3,3)=S'$
For $T(6,-4)$: $(6, -(-4))=(6,4)=T'$

Answer:

reflection across the x-axis