Use Coordinate Geometry to Solve Problems Quick Check

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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)
Responses

10 cm
10 cm

9 cm
9 cm

3 cm
3 cm

8 cm
8 cm
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Answer 1

To find the length of line segment \( BC \), we first need to determine the coordinates of points \( B \) and \( C \).

From the question, we have:

• \( B(1, 3) \)
• \( C(9, 3) \)

The points \( B \) and \( C \) both share the same \( y \)-coordinate (which is 3), meaning they lie on a horizontal line.

To find the length of line segment \( BC \), we can calculate the difference between the \( x \)-coordinates of points \( B \) and \( C \):

\[ \text{Length of } BC = |x_C - x_B| = |9 - 1| = 8 \]

Thus, the length of line segment \( BC \) is \( 8 \) cm.

The correct response is: 8 cm.