Question

1. which transformation is shown by the coordinates below? l(-1,9) m(-8,8) n(-3,5) l(-9,-1) m(-8,-8) n(-5,-3) a. reflection over the x - axis b. translation 8 units left and 8 units down c. rotation 90° clockwise d. rotation 270° clockwise

Explanation:

Step1: Recall transformation rules

For a point $(x,y)$ reflected over the x - axis, the new point is $(x, -y)$. For a 90° clock - wise rotation, $(x,y)\to(y,-x)$. For a 270° clock - wise rotation, $(x,y)\to(-y,x)$. For a translation $a$ units left and $b$ units down, $(x,y)\to(x - a,y - b)$.

Step2: Analyze given points

For point $L(-1,9)$ to $L'(-9,-1)$, for $M(-8,8)$ to $M'(-8,-8)$ and $N(-3,5)$ to $N'(-5,-3)$. If it was a reflection over the x - axis, the x - coordinates should stay the same, but they don't. If it was a translation 8 units left and 8 units down, $L(-1,9)$ would be $(-1 - 8,9 - 8)=(-9,1)$ which is incorrect. If it was a 90° clock - wise rotation, for $L(-1,9)$ we have $(x,y)=(-1,9)$ and $(y,-x)=(9,1)$ which is incorrect. If it was a 270° clock - wise rotation, for $L(-1,9)$ we have $(-y,x)=(-9,-1)$, for $M(-8,8)$ we have $(-y,x)=(-8,-8)$ and for $N(-3,5)$ we have $(-y,x)=(-5,-3)$.

Answer:

D. Rotation 270° clockwise