step by step solution:-

A is a point on the x-axis and B is on the y-axis

It means,

Coordinate of points A and B are :

A(x_1,0) ,B(0,y_1)

Also, it is given that **P(9,-8)** divides **AB** internally in the ratio** 4:3**

**Coordinates of a Point Between Two Points**

If point **C **is between points** A **and **B **in the coordinate system and the ratio** AC/AB **is given** **by** r=4/3**, the coordinates** **are:

x_1+r(x_2-x_1),y_1+r(y_2-y_1)

on substituting the values in the above formula

(\textcolor{primary}{9},\textcolor{secondary}{-8})=\left(\textcolor{primary}{x_{1}}+\textcolor{tertiary}{\frac{4}{3}}(\textcolor{primary}{0}-\textcolor{primary}{x_{1}}),\textcolor{secondary}{0}+\textcolor{tertiary}{\frac{4}{3}}(\textcolor{secondary}{y_{1}-0})\right)\implies x_1=-27 ,y_1=-6

hence,the required points are **A=(-27,0)** and** B=(0,-6)**

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