Bogged down trying to solve

All -- I have tried to solve the following problem to no avail; I keep getting bogged down. Any help appreciated.

Monty Central Florida USA

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The end points of a line segment in the x-y plane are at (1, 4) and (9, -12). What are the (x, y) points on the segment such that they divide it in the ratio 3:5 when all the possible cases are considered?

#Geometry

Easy Math Editor

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Comments

There are two possible cases to it.

Case 1: The point $(x,y)$ divides the line segment internally

Case 2: The point $(x,y)$ divides the line segment externally

There is a beautiful formula to it in coordinate geometry, about which you can see it from here.

The formula of the coordinates is $x=\dfrac{mx_2 \pm nx_1}{m \pm n}$ and $y=\dfrac{my_2\pm ny_1}{m\pm n}$ if the ratio is $m:n$ .

Use $+$ for Case 1 and use $-$ for Case 2.

Vilakshan Gupta - 3 years, 4 months ago

That is marvelous; I thank you very much.

Monty McGee

Monty McGee - 3 years, 4 months ago

Not a problem :)

Vilakshan Gupta - 3 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$