Question

what composition transformation rule has △lmn, l(1,1), m(7,2), and n(5,7) map onto △lmn. l(2, - 1), m(-4,0), and n(-2,5)? (1 point) a reflection across the y - axis and a move to the right by 3 and down by 2 a reflection across the y - axis and a move to the left by 5 and up by 3 a reflection across the x - axis and a move to the left by 3 and down by 2 a rotation of 270 degrees clockwise and a move right by 3 and up by 2

Explanation:

Step1: Analyze reflection across y - axis

The rule for reflecting a point $(x,y)$ across the $y$-axis is $(x,y)\to(-x,y)$. For point $L(1,1)$, after reflection across the $y$-axis, it becomes $(- 1,1)$. For $M(7,2)$, it becomes $(-7,2)$ and for $N(5,7)$ it becomes $(-5,7)$.

Step2: Analyze translation

If we consider the translation after reflection across the $y$-axis. Let's check the first option of moving right by 3 and down by 2.
For the reflected point of $L(-1,1)$, after moving right by 3 ($x$ - value increases by 3) and down by 2 ($y$-value decreases by 2), we get $(-1 + 3,1-2)=(2,-1)$.
For the reflected point of $M(-7,2)$, after moving right by 3 and down by 2, we get $(-7 + 3,2 - 2)=(-4,0)$.
For the reflected point of $N(-5,7)$, after moving right by 3 and down by 2, we get $(-5+3,7 - 2)=(-2,5)$.

Answer:

a reflection across the y - axis and a move to the right by 3 and down by 2