The coordinates of the point are (12.6 , 6.8)
Step-by-step explanation:
If point (x , y) partitions the directed line segment at a ratio [tex]m_{1}:m_{2}[/tex] , and the endpoints of the segment are [tex](x_{1},y_{1})[/tex] , [tex](x_{2},y_{2})[/tex] , then
- [tex]x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}[/tex]
- [tex]y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}[/tex]
∵ Point G is located at (3 , 2)
∵ Point H is located at (15 , 8)
- The endpoints of the segments are G and H
∴ [tex]x_{1}[/tex] = 3 and [tex]x_{2}[/tex] = 15
∴ [tex]y_{1}[/tex] = 2 and [tex]y_{2}[/tex] = 8
∵ A point partitions GH in a 4 : 1 ratio
∴ [tex]m_{1}[/tex] = 4 and [tex]m_{2}[/tex] = 1
- Use the rules above to find the coordinates of this point
∵ [tex]x=\frac{(3)(1)+(15)(4)}{4+1}=\frac{3+60}{5}=12.6[/tex]
∴ The x-coordinate of the point is 12.6
∵ [tex]y=\frac{(2)(1)+(8)(4)}{4+1}=\frac{2+32}{5}=6.8[/tex]
∴ The y-coordinate of the point is 6.8
The coordinates of the point are (12.6 , 6.8)
Learn more:
You can learn more about the point of partitions in brainly.com/question/11280112
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