Answer :
The mid-point of the line segment is (2 , [tex]\frac{6}{5}[/tex] )
Step-by-step explanation:
If (x , y) is the mid-point of a segment whose end points are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] , then
- [tex]x=\frac{x_{1}+x_{2}}{2}[/tex]
- [tex]y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ The end-points of a line segment are (6 , [tex]\frac{3}{5}[/tex] ) and (-2 , [tex]\frac{9}{5}[/tex] )
∴ [tex]x_{1}[/tex] = 6 and [tex]x_{2}[/tex] = -2
∴ [tex]y_{1}[/tex] = [tex]\frac{3}{5}[/tex] and [tex]y_{2}[/tex] = [tex]\frac{9}{5}[/tex]
∵ [tex]x=\frac{x_{1}+x_{2}}{2}[/tex]
∴ [tex]x=\frac{6+(-2)}{2}[/tex]
∴ [tex]x=\frac{6-2}{2}[/tex]
∴ [tex]x=\frac{4}{2}[/tex]
∴ x = 2
∴ The x-coordinate of the mid-point is 2
∵ [tex]y=\frac{y_{1}+y_{2}}{2}[/tex]
∴ [tex]y=\frac{\frac{3}{5}+\frac{9}{5}}{2}[/tex]
∴ [tex]y=\frac{\frac{12}{5}}{2}[/tex]
∴ [tex]y=\frac{12}{10}[/tex]
- Divide up and down by 2 to reduce the fraction to its lowest value
∴ [tex]y=\frac{6}{5}[/tex]
∴ The y-coordinate of the mid-point is [tex]\frac{6}{5}[/tex]
The mid-point of the line segment is (2 , [tex]\frac{6}{5}[/tex] )
Learn more:
You can learn more about the mid-point in brainly.com/question/5223123
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