Problem Analysis:

The problem involves a rectangle $ABCD$ where:

• $AB$ is parallel to the $x$-axis.
• The coordinates of $B$ are given as $B(2, 1)$.
• We need to find the equation of line $BC$.

Key Observations:

1. Since $AB$ is parallel to the $x$-axis, $A$ and $B$ must have the same $y$-coordinate, which is $y = 1$.
2. $BC$ is a vertical line, as the sides of a rectangle are either horizontal or vertical.
3. A vertical line has an equation of the form $x = c$, where $c$ is the constant $x$-coordinate of the line.

Solving:

From the diagram:

• Point $B$ is at $(2, 1)$.
• $C$ lies directly below $B$ on a vertical line, so $BC$ has the equation: $x = 2$

Final Answer:

The equation of line $BC$ is: $x = 2$

Would you like a detailed explanation of how vertical and horizontal line equations are derived? Let me know!

Related Questions:

1. How can you determine the equation of line $AD$ for this rectangle?
2. What is the length of side $BC$ if the coordinates of $C$ are known?
3. If $C$ is at $(2, -3)$, what is the area of rectangle $ABCD$?
4. How can you find the midpoint of diagonal $AC$?
5. How does the slope of line $AB$ compare to that of line $BC$?

Tip:

For vertical lines, the slope is undefined, as the difference in $x$-values is zero, leading to division by zero when computing slope!