Question
If A (-14, -10), B(6, -2) is given, find the coordinates of the points whichdivide segment AB into four equal parts.
✓
Answer
let the points dividing AB be C,D,E.
AC:CD:DE:EB∷1:1:1:1
A point P(x,y) divides the line formed by points (a,b) and (c,d) in the ratio of m:n, then the coordinates of the point P is given by
$x =\frac{ an + cm }{ m + n } \text { and } y =\frac{ bn + dm }{ m + n }$
$\text { For } C m:n :: 1: 3$
$x =\frac{(-14) 3+(6) 1}{1+3}=-9$
$y =\frac{(-10) 3+(-2) 1}{1+3}=-8$
For D m:n ::2:2
$x=\frac{(-14) 2+(6) 2}{2+2}=-4$
$y=\frac{(-10) 2+(-2) 2}{2+2}=-6$
For E m:n :: 3:1
$x=\frac{(-14) 1+(6) 3}{3+1}=1$
$y=\frac{(-10) 1+(-2) 3}{1+3}=-4$
Hence coordinates of $C=(-9,-8)$
$D=(-4,-6)$
$E=(1,-4)$
AC:CD:DE:EB∷1:1:1:1
A point P(x,y) divides the line formed by points (a,b) and (c,d) in the ratio of m:n, then the coordinates of the point P is given by
$x =\frac{ an + cm }{ m + n } \text { and } y =\frac{ bn + dm }{ m + n }$
$\text { For } C m:n :: 1: 3$
$x =\frac{(-14) 3+(6) 1}{1+3}=-9$
$y =\frac{(-10) 3+(-2) 1}{1+3}=-8$
For D m:n ::2:2
$x=\frac{(-14) 2+(6) 2}{2+2}=-4$
$y=\frac{(-10) 2+(-2) 2}{2+2}=-6$
For E m:n :: 3:1
$x=\frac{(-14) 1+(6) 3}{3+1}=1$
$y=\frac{(-10) 1+(-2) 3}{1+3}=-4$
Hence coordinates of $C=(-9,-8)$
$D=(-4,-6)$
$E=(1,-4)$
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