The coordinates of point P are (-3 , -6)
Step-by-step explanation:
If point (x , y) partitions line AB where A = [tex](x_{1},y_{1})[/tex] and B = [tex](x_{2},y_{2})[/tex]
at a ratio [tex]m_{1}:m_{2}[/tex] from A then:
1. [tex]x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}[/tex]
2. [tex]y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}[/tex]
∵ P partitions AB in the ratio 3 : 4
∴ [tex]m_{1}:m_{2}[/tex] = 3 : 4
∵ A = (-9 , -9) and B = (5 , -2)
- Substitute the coordinates of points A and B in the rules above
∵ [tex]x=\frac{(-9)(4)+(5)(3)}{3+4}[/tex]
∴ [tex]x=\frac{-36+15}{7}[/tex]
∴ [tex]x=\frac{-21}{7}[/tex]
∴ x = -3
The x-coordinate of P is -3
∵ [tex]y=\frac{(-9)(4)+(-2)(3)}{3+4}[/tex]
∴ [tex]y=\frac{-36+(-6)}{7}[/tex]
∴ [tex]y=\frac{-42}{7}[/tex]
∴ y = -6
The y-coordinate of P is -6
The coordinates of point P are (-3 , -6)
Learn more:
You can learn more about the mid-point of a segment in brainly.com/question/5223123
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