To find the length of line segment \( BC \), we'll use the coordinates of points \( B \) and \( C \), which are given as \( B(1, 3) \) and \( C(9, 3) \).
The length of a line segment with endpoints \((x1, y1)\) and \((x2, y2)\) can be found using the distance formula:
\[ \text{Distance} = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \]
For line segment \( BC \):
- \((x1, y1) = (1, 3)\)
- \((x2, y2) = (9, 3)\)
Substitute these coordinates into the distance formula:
\[ \text{Distance} = \sqrt{(9 - 1)^2 + (3 - 3)^2} \]
Simplify inside the square root:
\[ \text{Distance} = \sqrt{(8)^2 + (0)^2} \]
\[ \text{Distance} = \sqrt{64 + 0} \]
\[ \text{Distance} = \sqrt{64} \]
\[ \text{Distance} = 8 \]
Therefore, the length of line segment \( BC \) is 8 units.
Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane with the x axis extending from 0 to 9 and the y axis extending from 0 to 9 in increments of 1. A quadrilateral upper A upper B upper C upper D is drawn on the coordinate plane. The coordinates of the rectangle are as follows: upper A left parenthesis 2 comma 5 right parenthesis, upper B left parenthesis 1 comma 3 right parenthesis, upper C left parenthesis 9 comma 3 right parenthesis, and upper D left parenthesis 9 comma 6 right parenthesis.
Find the length of line segment BC .
(1 point)
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