To determine the equation of the diagonal line [tex]\(BC\)[/tex] of the square, we need to follow these steps:
1. Identify the coordinates of points B and C:
- [tex]\(B(3, 3)\)[/tex]
- [tex]\(C(3, -3)\)[/tex]
2. Calculate the slope of line BC:
The slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the coordinates of B and C:
[tex]\[
m = \frac{-3 - 3}{3 - 3}
\][/tex]
However, notice that the x-coordinates of B and C are the same ([tex]\(3\)[/tex]). This indicates that the line BC is vertical.
3. Equation of a vertical line:
For any vertical line, the equation is simply [tex]\(x = k\)[/tex], where [tex]\(k\)[/tex] is the constant x-coordinate value of any point on the line.
Since both points B and C have an x-coordinate of [tex]\(3\)[/tex], the equation of the line BC in standard form is:
[tex]\[
x = 3
\][/tex]
Therefore, the equation of the diagonal line BC in standard form is:
[tex]\[
x = 3
\][/tex]
