Question

Two vertices of a triangle have coordinates (3, 4) and (-4, -6). If the centroid of

the triangle is at the origin. What are the coordinates of the third vertex.​

Answer 1

Given :

• Two vertices of a triangle have coordinates (3, 4) and (-4, -6).

To Find :

• Coordinates of the third vertex.

Solution :

So, Let's take

• x1 = 3, x2 = -4
• y1 = 4, y2 = -6

By using Centroid formula,

$\tt \longrightarrow \: \: centroid \: = ( \dfrac{x1 + x2 + x3}{3} , \dfrac{y1 + y2 + y3}{3} )$

$\tt \longrightarrow \: centroid \: = ( \dfrac{3 + ( - 4) + x3}{3} , \dfrac{4 + ( - 6) + y3}{3} )$

$\tt \longrightarrow \: centroid \: = ( \dfrac{3 - 4 + x3}{3} , \dfrac{4 - 6 + y3}{3} )$

$\tt \longrightarrow \: centroid \: = ( \dfrac{ - 1+ x3}{3} , \dfrac{ - 2 + y3}{3} )$

$\tt \longrightarrow \: centroid \: = ( \ - 1 + x3 , - 2 + y3 )$

$\tt \longrightarrow -1+x3 \: \: \: \: \: \: \: \: \: \: \longrightarrow \: -2+y3$

$\tt \longrightarrow 1 = x3 \: \: \: \: \: \: \: \: \: \: \longrightarrow \: 2 = y3$

•°• The coordinates of third vertices are ( 1 , 2 )