To solve the problem of reflecting the triangle $\triangle ABC$ across the y-axis, we need to find the coordinates of the reflected points $A'$, $B'$, and $C'$.

Step-by-step Solution:

1. Identify the Coordinates of Points A, B, and C:

   • From the image, let's determine the coordinates of points $A$, $B$, and $C$.
     • Point $A$ is at $(4, 2)$.
     • Point $B$ is at $(2, -1)$.
     • Point $C$ is at $(0, -3)$.

2. Reflection Across the Y-Axis:

   • When reflecting a point across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same.
   • If a point $(x, y)$ is reflected across the y-axis, it becomes $(-x, y)$.

3. Find the Coordinates of $A'$, $B'$, and $C'$:

   • For point $A$ at $(4, 2)$, the reflected point $A'$ will be $(-4, 2)$.
   • For point $B$ at $(2, -1)$, the reflected point $B'$ will be $(-2, -1)$.
   • For point $C$ at $(0, -3)$, the reflected point $C'$ will be $(0, -3)$ (since it is on the y-axis, its reflection is the same).

Conclusion:

The coordinates of the reflected points $A'B'C'$ are:

• $A'(-4, 2)$
• $B'(-2, -1)$
• $C'(0, -3)$

Would you like any additional details or have any questions?

Related Questions to Explore:

1. What is the rule for reflecting points across the x-axis?
2. How do you reflect a shape over the line $y = x$?
3. What are the coordinates if the triangle $ABC$ is reflected over the line $y = -x$?
4. How would you calculate the area of triangle $ABC$ before and after reflection?
5. How can you translate a shape to a new position on the coordinate plane?

Tip:

When reflecting a point across any line, remember that only the coordinate perpendicular to that line changes sign.