Question

Find the coordinates of the points which divides the line segment joining A(-4,2) and B(4,8) into four equal parts

Answer 1

$\bf \underline{GIVEN}$

• Coordinates of A= (-4,2)
• Coordinates of B = (4,8)
• A and B divides the line into four equal parts.

$\bf \underline{TO \: FIND}$

• Coordinates of the other points on line segment.

$\bf \underline{SOLUTION}$

Let the other parts be C, D and E.

➸ Mid point formula,

$\boxed{ \bf for \: x \to \: \dfrac{ x_{1} +x_{2} }{2}} \:$

$\boxed{ \bf for \: y \to \: \dfrac{ y_{1} +y_{2} }{2}} \:$

ㅤ

∵ D is the mid point of AB,

$\sf \: coordinates \: of \: D = ( \dfrac{ -4+4}{2} )( \dfrac{2+8}{2} )$

$\small \implies \boxed {\boxed {\tt \blue {D(0,5) }}}$

∵ C is the mid point of AD,

$\sf coordinates \: of \: C= (\dfrac{ -4+0}{2} ),( \dfrac{2+5}{2})$

$\small \implies \boxed {\boxed {\tt \blue {C(-2, \frac{7}{2}) }}}$

∵E is the mid point of BD,

$\sf \: coordinates \: of \: E = ( \dfrac{ 0+4 }{2} )( \dfrac{5+8}{2} )$

$\small \implies \boxed {\boxed {\tt \blue {E(0,\frac{13}{2} ) }}}$