Help: Dividing line with ratio

A segment $PQ$ with $2.1$ in length divided by point $X$ so that $ \dfrac{PX}{XQ} = \dfrac{4}{3}$ and by point $Y$ so that $\dfrac{PY}{YQ} = -\dfrac{4}{3}$. Find $XY$.

#Geometry

Easy Math Editor

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`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}`	$\boxed{123}$

Comments

We use the formulae for internal and external division of a line segment in a ratio:

If the division is $\frac {m}{n}$ of segment $AB$ and the internal point is $C$ and the external point is $D$ , the internal length $BC$ is $\frac {n}{m+n} AB$ and the external length $BD$ is $\frac {n}{m-n}$ .

Try to prove these formulae. We have

$QX=\frac {3}{4+3} PQ \Rightarrow QX = 0.9$

$QY = \frac {3}{4-3} PQ \Rightarrow QY = 6.3$

Thus, $QX+QY=XY=7.2$ .

Sharky Kesa - 4 years, 10 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}`	$\boxed{123}$