Question

Can someone help me please?

Answer 1

Given:

A line segment AB.

A point is
`(3)/(10)` of the way from A to B.

To find:

The coordinates of that point.

Solution:

Section formula: If a point divide a line segment in m:n, then

`Point=\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\right)`

From the given figure, it is clear that the two end points of the line segment are A(-4,-5) and B(12,4).

Let the unknown point be P. The point is
`(3)/(10)` of the way from A to B. It means,

`(AP)/(AB)=(3)/(10)`

Let AP and AB are 3x and 10x, then

`(AP)/(PB)=(AP)/(AB-AP)`

`(AP)/(PB)=(3x)/(10x-3x)`

`(AP)/(PB)=(3x)/(7x)`

`(AP)/(PB)=(3)/(7)`

It means, point P divided the line segment in 3:7.

Using section formula, we get

`P=\left((3(12)+7(-4))/(3+7),(3(4)+7(-5))/(3+7)\right)`

`P=\left((36-28)/(10),(12-35)/(10)\right)`

`P=\left((8)/(10),(-23)/(10)\right)`

`P=\left(0.8,-2.3\right)`

Therefore, the coordinates of the required point are (0.8, -2.3).