Reflect triangle a in the x axis to give triangle b. Then rotate your triangle b 90 degrees clockwise around the origin to give triangle c. Describe fully the single transformation that maps triangle a onto c

The single transformation that maps a onto c is the reflection of the triangle a  about the line y = -x

Step-by-step explanation:

To answer the question, we note that the result of reflection of a point (x, y) across the x axis is given as follows;

Coordinates before reflection = (x, y), Coordinates after reflection = (x, -y)

Also, when we rotate a  point, (x, y), 90° clockwise, we have;

Image point before 90° clockwise rotation = (x, y), Image point after 90° clockwise rotation = (y, -x)

Therefore, the rotation of the point (x, -y), 90° clockwise will give

Image point before 90° clockwise rotation = (x, -y), Image point after 90° clockwise rotation = (-y, -x)

Which gives the combined transformation as (x, y) → (-y, -x) which is the rule equivalent to reflection about the line y = -x.