Linear Equations II

Hong Kong

Stage 4 - Stage 5

Point $P$`P` divides the interval joining the points $\left(x_1,y_1\right)$(`x`1,`y`1) and $\left(x_2,y_2\right)$(`x`2,`y`2) in the ratio $m:n$`m`:`n`. Which of the following formulas gives the $x$`x`-coordinate of point $P$`P`?

$\frac{-mx_2+nx_1}{m+n}$−`m``x`2+`n``x`1`m`+`n`

A

$\frac{mx_1+nx_2}{m+n}$`m``x`1+`n``x`2`m`+`n`

B

$\frac{mx_2+nx_1}{m+n}$`m``x`2+`n``x`1`m`+`n`

C

$\frac{mx_1-nx_2}{m+n}$`m``x`1−`n``x`2`m`+`n`

D

Easy

< 1min

Point $P$`P` divides the interval joining the points $\left(x_1,y_1\right)$(`x`1,`y`1) and $\left(x_2,y_2\right)$(`x`2,`y`2) in the ratio $m:n$`m`:`n`. Which of the following formulas gives the $y$`y`-coordinate of point $P$`P`?

Easy

< 1min

When the point $P$`P` divides the interval $AB$`A``B` internally, is the ratio $m$`m`:$n$`n` (that is used in calculations) positive or negative?

Easy

< 1min

When the point $P$`P` divides the interval $AB$`A``B` externally, is the ratio $m$`m`:$n$`n` positive or negative?

Easy

< 1min

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