To find the length of line segment BC, we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of points B and C.
Given the coordinates of points B and C:
- B(1, 3)
- C(9, 3)
Now, applying the distance formula:
\[ d_{BC} = \sqrt{(9 - 1)^2 + (3 - 3)^2} \]
Calculating the values inside the square root:
\[ d_{BC} = \sqrt{(8)^2 + (0)^2} \]
\[ d_{BC} = \sqrt{64 + 0} \]
\[ d_{BC} = \sqrt{64} \]
\[ d_{BC} = 8 \]
Thus, the length of line segment BC is \( \text{8 cm} \).