Question

which sequence of transformations maps jkl onto jkl? a translation right 1 unit and down 11 units followed by a reflection across the y - axis a translation right 1 unit and up 4 units followed by a rotation 180° around the origin a translation right 5 units and up 4 units followed by a reflection across the x - axis

Explanation:

Step1: Analyze translation

Let's assume a point $(x,y)$ in $\triangle{JKL}$. For a translation right 1 unit and down 11 units, the transformation rule is $(x,y)\to(x + 1,y-11)$.

Step2: Analyze reflection across y - axis

The rule for reflection across the y - axis is $(x,y)\to(-x,y)$.
Let's take point $J(0,6)$. After translation right 1 unit and down 11 units, it becomes $(0 + 1,6-11)=(1,-5)$. After reflection across the y - axis, it becomes $(-1,-5)$.
Let's check other points. For point $K(-1,1)$, after translation right 1 unit and down 11 units, it becomes $(-1 + 1,1-11)=(0,-10)$. After reflection across the y - axis, it becomes $(0,-10)$.
For point $L(-4,1)$, after translation right 1 unit and down 11 units, it becomes $(-4 + 1,1-11)=(-3,-10)$. After reflection across the y - axis, it becomes $(3,-10)$.
We can verify that these new - found points match the coordinates of $\triangle{J'K'L'}$.

Answer:

a translation right 1 unit and down 11 units followed by a reflection across the y - axis