Question

line segment with one endpoint at (2,5) is divided in the ratio 4:5 by the point (10,1). which coordinates could represent the other endpoint.

Answer 1

Answer:

(20,-4)

Step-by-step explanation:

We are given;

One end point as (2,5)

Point of division as (10,1)

The ratio of division as 4:5

We are required to calculate the other endpoint.

Assuming the other endpoint is (x,y)

Using the ratio theorem

If the unknown endpoint is the last point on the line segment;

Then;

$\left[\begin{array}{ccc}10\\1\end{array}\right]$=$\frac{4}{5} \left[\begin{array}{ccc}x\\y\end{array}\right]$+$\frac{5}{9}\left[\begin{array}{ccc}2\\5\end{array}\right]$

Therefore; solving the equation;

$10=\frac{4}{9}x+\frac{10}{9}$

solving for x

x = 20

Also

$1=\frac{4}{9}y+\frac{25}{9}$

solving for y

y= -4

Therefore,

the coordinates of the end point are (20,-4)