Two vertices of a triangle are at (-3,1)& (0,2) and centroid is at origin , find its third vertex

Two vertices of a triangle are at (-3,1)& (0,2) and centroid is at ori

1.	Two vertices of a triangle are at (-3,1)& (0,2) and centroid is at origin , find its third vertex
Answer» Let the coordinates of the third vertex be (x, y). Then by centroid formula, coordinates of centroid of given triangle are,{tex}\\left( \\frac { x - 3 + 0 } { 3 } , \\frac { y + 1 - 2 } { 3 } \\right) = \\left( \\frac { x - 3 } { 2 } , \\frac { y - 1 } { 3 } \\right){/tex}We have centorid is at origin (0, 0){tex}\\therefore \\frac { x - 3 } { 3 } = 0 \\quad \\text { and } \\frac { y - 1 } { 3 } = 0{/tex}{tex}\\Rightarrow{/tex}x - 3 = 0\xa0{tex}\\Rightarrow{/tex}y - 1 = 0{tex}\\Rightarrow{/tex}x = 3{tex}\\Rightarrow{/tex}y = 1Hence, the coordinates of the third vertex are (3, 1).