Question

△jkl is translated using (x, y)→(x + 1,y - 3) and reflected across the x - axis. what are the coordinates of the final image of point j under this composition of transformations? (-9,7) (1,-1) (-1,1) (1,1)

Explanation:

Step1: Determine initial coordinates of J

From the graph, the coordinates of point J are $(0, 2)$.

Step2: Apply translation

The translation rule is $(x,y)\to(x + 1,y - 3)$. For point J with $x = 0$ and $y=2$, we have $x'=0 + 1=1$ and $y'=2-3=-1$. So the coordinates after translation are $(1,-1)$.

Step3: Apply reflection across x - axis

The rule for reflecting a point $(x,y)$ across the x - axis is $(x,y)\to(x,-y)$. For the point $(1,-1)$, after reflection, the x - coordinate remains the same ($x = 1$) and the y - coordinate becomes $-(-1)=1$. So the final coordinates are $(1,1)$.

Answer:

$(1,1)$