Question

Find the midpoint of the line segment with the given endpoints.

Answer 1

The mid-point of the line segment is (2 , $\frac{6}{5}$ )

Step-by-step explanation:

If (x , y) is the mid-point of a segment whose end points are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ , then

• $x=\frac{x_{1}+x_{2}}{2}$

• $y=\frac{y_{1}+y_{2}}{2}$

∵ The end-points of a line segment are (6 , $\frac{3}{5}$ ) and (-2 , $\frac{9}{5}$ )

∴ $x_{1}$ = 6 and $x_{2}$ = -2

∴ $y_{1}$ = $\frac{3}{5}$ and $y_{2}$ = $\frac{9}{5}$

∵ $x=\frac{x_{1}+x_{2}}{2}$

∴ $x=\frac{6+(-2)}{2}$

∴ $x=\frac{6-2}{2}$

∴ $x=\frac{4}{2}$

∴ x = 2

∴ The x-coordinate of the mid-point is 2

∵ $y=\frac{y_{1}+y_{2}}{2}$

∴ $y=\frac{\frac{3}{5}+\frac{9}{5}}{2}$

∴ $y=\frac{\frac{12}{5}}{2}$

∴ $y=\frac{12}{10}$

- Divide up and down by 2 to reduce the fraction to its lowest value

∴ $y=\frac{6}{5}$

∴ The y-coordinate of the mid-point is $\frac{6}{5}$

The mid-point of the line segment is (2 , $\frac{6}{5}$ )

Learn more:

You can learn more about the mid-point in brainly.com/question/5223123

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