Question

the graph shows pentagons lm nop and lmnop. which sequence of transformations maps lm nop onto lmnop? a rotation 90° clockwise around the origin followed by a translation right 1 unit and down 7 units a reflection across the x - axis followed by a rotation 90° counterclockwise around the origin a translation down 7 units followed by a reflection across the y - axis

Explanation:

Step1: Recall rotation rules

A 90 - degree clock - wise rotation around the origin $(x,y)\to(y, - x)$.

Step2: Consider translation

A translation right 1 unit and down 7 units means $(x,y)\to(x + 1,y-7)$.
Let's assume a point $(x,y)$ on LM NOP. After 90 - degree clock - wise rotation around the origin, it becomes $(y,-x)$. Then after translation right 1 unit and down 7 units, it becomes $(y + 1,-x-7)$.
For a reflection across the x - axis, $(x,y)\to(x,-y)$. Then a 90 - degree counter - clockwise rotation around the origin $(x,-y)\to(y,x)$ which does not match the transformation.
For a translation down 7 units $(x,y)\to(x,y - 7)$ and then a reflection across the y - axis $(x,y - 7)\to(-x,y - 7)$ which also does not match.

Answer:

a rotation 90° clockwise around the origin followed by a translation right 1 unit and down 7 units