Question

Find the coordinates of P so that P partitions AB in the ratio 3:4 with A(-9,-9) and B(5,-2).

Answer 1

The coordinates of point P are (-3 , -6)

Step-by-step explanation:

If point (x , y) partitions line AB where A = $(x_{1},y_{1})$ and B = $(x_{2},y_{2})$

at a ratio $m_{1}:m_{2}$ from A then:

1. $x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

2. $y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

∵ P partitions AB in the ratio 3 : 4

∴ $m_{1}:m_{2}$ = 3 : 4

∵ A = (-9 , -9) and B = (5 , -2)

- Substitute the coordinates of points A and B in the rules above

∵ $x=\frac{(-9)(4)+(5)(3)}{3+4}$

∴ $x=\frac{-36+15}{7}$

∴ $x=\frac{-21}{7}$

∴ x = -3

The x-coordinate of P is -3

∵ $y=\frac{(-9)(4)+(-2)(3)}{3+4}$

∴ $y=\frac{-36+(-6)}{7}$

∴ $y=\frac{-42}{7}$

∴ 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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