Question

what composition transformation rule has △lmn, l(8,3), m (4,6), and n (5,9) map onto △ lmn, l(-10,-3), m(-6,0), and n(-7,3)? (1 point)

a rotation of 270 degrees clockwise and a move right by 2 and up by 6

a reflection over the y - axis and a move to the left by 6 and down by 2

a reflection across the x - axis and a move to the right by 2 and down by 6

a reflection over the y - axis and a move to the left by 2 and down by 6

Explanation:

Step1: Analyze reflection over y - axis

The rule for reflecting a point $(x,y)$ over the y - axis is $(x,y)\to(-x,y)$. For point $L(8,3)$, after reflection over the y - axis, it becomes $(-8,3)$. For $M(4,6)$, it becomes $(-4,6)$ and for $N(5,9)$ it becomes $(-5,9)$.

Step2: Analyze translation

We want to get from $(-8,3)$ to $(-10,-3)$, from $(-4,6)$ to $(-6,0)$ and from $(-5,9)$ to $(-7,3)$. The translation rule from $(x_1,y_1)$ to $(x_2,y_2)$ is $(x_2 - x_1,y_2 - y_1)$. For the x - coordinates: $-10-(-8)=-2$, $-6 - (-4)=-2$, $-7-(-5)=-2$. For the y - coordinates: $-3 - 3=-6$, $0 - 6=-6$, $3 - 9=-6$. So the translation is 2 units left and 6 units down.

Answer:

D. a reflection over the y - axis and a move to the left by 2 and down by 6