Mathematics: What are the coordinates of the point on the directed line segment from (3, -1)(3,−1) to (9, 8)(9,8) that partitions the segment into a ratio of 1 to 2?

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What are the coordinates of the point on the directed

svarner2001

24.01.2022

Coordinates of the point on the directed line segment is (15/3,7/3)

Step-by-step explanation:

Given:

A line segment with coordinates partition in some ratio.

Lets say that the ends of the segment are A and B.

We have to find the coordinates of C.

Coordinates of point A are = (3,-1)

Coordinates of point B are = (9,8)

Considering the point C as (x,y) and the partition ratios as m:n i.e 1:2

Formula to be used:

Section formula:

$x= \frac{mx_2+n_x_1}{m+n},\ y=\frac{my_2+ny_1}{m+n}$

Using the above formula.

⇒ $x= \frac{mx_2+n_x_1}{m+n},\ y=\frac{my_2+ny_1}{m+n}$

⇒ Plugging the values.

⇒ $x= \frac{1(9)+2(3)}{1+2},\ y=\frac{1(8)+2(-1)}{1+2}$

⇒ $x= \frac{9+6}{3},\ y=\frac{9-2}{3}$

⇒ $x= \frac{15}{3},\ y=\frac{7}{3}$ or

⇒ $x= 5,\ y=2.3$

The coordinates of the point on the directed line segment is (15/3,7/3) in terms of decimals it is (5,2.3).

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