Subjects geometry

Line Segments E16201

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1. The problem is to find or understand 2 line segments. 2. A line segment is a part of a line bounded by two distinct endpoints. 3. To define a line segment, you need the coordinates of its two endpoints. 4. For example, if the endpoints are $A(x_1,y_1)$ and $B(x_2,y_2)$, the line segment is the set of points between $A$ and $B$. 5. The length of the line segment $AB$ is given by the distance formula: $$\text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 6. If you want to find the midpoint $M$ of the segment $AB$, use: $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$ 7. To create two line segments, you need two pairs of endpoints. 8. For example, line segment $AB$ with endpoints $A(1,2)$ and $B(4,6)$, and line segment $CD$ with endpoints $C(0,0)$ and $D(3,3)$. 9. Calculate lengths: $$AB = \sqrt{(4-1)^2 + (6-2)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$ $$CD = \sqrt{(3-0)^2 + (3-0)^2} = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}$$ 10. Thus, you have two line segments $AB$ and $CD$ with lengths 5 and $3\sqrt{2}$ respectively.