The x - and y - coordinates of point P are ( - 1 , 2 )
The standard form of the linear equation is,
![y=mx+c](https://tex.z-dn.net/?f=y%3Dmx%2Bc)
Where
is the gradient of the line.
Given-
P is 2/3 the length of the line segment from A to B. Suppose
is two, then
![m+n=3](https://tex.z-dn.net/?f=m%2Bn%3D3)
This gradient of the line can be calculated with the following formula-
![m=\dfrac{y_{2}-y_{1} }{x_{2}- x_{1} }](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_%7B2%7D-y_%7B1%7D%20%7D%7Bx_%7B2%7D-%20x_%7B1%7D%20%7D)
Here, (
) and (
) are two arbitrary points.
In the given graph, at point A(9,-8),
![x_{1} =9](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D9)
![y_{1} =-8](https://tex.z-dn.net/?f=y_%7B1%7D%20%3D-8)
At point B (-6,7),
![x_{2} =-6](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D-6)
![y_{2} =7](https://tex.z-dn.net/?f=y_%7B2%7D%20%3D7)
Use the formula has given in the problem which is,
![x=\dfrac{m}{m+n}(x_{2} -x_{1} )+x_{1}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7Bm%7D%7Bm%2Bn%7D%28x_%7B2%7D%20-x_%7B1%7D%20%29%2Bx_%7B1%7D)
Put the values,
![x=\dfrac{2}{3}(-6 -9 )+9](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B2%7D%7B3%7D%28-6%20-9%20%29%2B9)
![x=\dfrac{2}{3}(-15 )+9](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B2%7D%7B3%7D%28-15%20%29%2B9)
![x=2(-5 )+9](https://tex.z-dn.net/?f=x%3D2%28-5%20%29%2B9)
![x=-10+9](https://tex.z-dn.net/?f=x%3D-10%2B9)
![x=-1](https://tex.z-dn.net/?f=x%3D-1)
For y use the formula given in the problem which is
![y=\dfrac{m}{m+n}(y_{2} -y_{1} )+y_{1}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7Bm%7D%7Bm%2Bn%7D%28y_%7B2%7D%20-y_%7B1%7D%20%29%2By_%7B1%7D)
![y=\dfrac{2}{3}(7 -(-8) )+(-8)](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B2%7D%7B3%7D%287%20-%28-8%29%20%29%2B%28-8%29)
![y=\dfrac{2}{3}(7+8) )-8](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B2%7D%7B3%7D%287%2B8%29%20%29-8)
![y=\dfrac{2}{3}(15) )-8](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B2%7D%7B3%7D%2815%29%20%29-8)
![y={2}(5) -8](https://tex.z-dn.net/?f=y%3D%7B2%7D%285%29%20-8)
![y=2](https://tex.z-dn.net/?f=y%3D2)
Hence, the x - and y - coordinates of point P are ( - 1 , 2 )
For more about the coordinates, follow the link below-
brainly.com/question/13140132