A is a point on the x-axis and B is a point on the y-axis. P is (9,-8) and P divides [AB] internally in the ratio 4:3.Find the coordinates of A and B.

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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