10.03 Dividing a segment into a given ratio
Interactive practice questions
Point $P$P divides the interval joining the points $\left(x_1,y_1\right)$(x1,y1) and $\left(x_2,y_2\right)$(x2,y2) in the ratio $m:n$m:n. Which of the following formulas gives the $x$x-coordinate of point $P$P?
$\frac{-mx_2+nx_1}{m+n}$−mx2+nx1m+n
$\frac{mx_1+nx_2}{m+n}$mx1+nx2m+n
$\frac{mx_2+nx_1}{m+n}$mx2+nx1m+n
$\frac{mx_1-nx_2}{m+n}$mx1−nx2m+n
Point $P$P divides the interval joining the points $\left(x_1,y_1\right)$(x1,y1) and $\left(x_2,y_2\right)$(x2,y2) in the ratio $m:n$m:n. Which of the following formulas gives the $y$y-coordinate of point $P$P?
When the point $P$P divides the interval $AB$AB internally, is the ratio $m$m:$n$n (that is used in calculations) positive or negative?
When the point $P$P divides the interval $AB$AB externally, is the ratio $m$m:$n$n positive or negative?