Class 10

Math

All topics

Coordinate Geometry

Find the lengths of the medians AD and BE of $ΔABC$ whose vertices are $A(7,−3),B(5,3)$ and $C(3,−1)$.

Vertices of $ΔABC$ are $A(7,−3),B(5,3)$ and $C(3,−1)$

From figure: BE and AD are the medians of triangle.

Find Coordinates of E and D:

Coordinates of E$=(23+7 ,2−1−3 )$

$=(5,−2)$

Coordinates of $D=(23+5 ,2−1+3 )$

$=(4,1)$

Find AD and BE using distance formula:

$AD=(x_{2}−x_{1})_{2}+(y_{2}−y_{1})_{2} $

$=(7−4)_{2}+(3+1)_{2} $

$=3_{2}+4_{2} $

$=9+16 $

$=25 $

$=5$ units.

and $BE=(5−5)_{2}+(3+2)_{2} =0_{2}+5_{2} $

$=25 =5$ units

Therefore, $BE=5$ units and $AD=5$ units.(both are equal)