Can someone help me please?

Question

asked Mar 11, 2022 217k views

1 Answer

Nick Farina · Answer 1 · 2022-03-16T11:27:55+0000

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).