Exam

JEE Main

Year

2019

Date

12 April

Shift

Evening Shift

Subject

Mathematics

Chapter

Straight Lines

JEE Main 2019 · 12 April · Evening Shift · Mathematics · Straight Lines

A triangle has a vertex at ( 1, 2 ) and the mid points of the two...

A triangle has a vertex at $( 1, 2 )$ and the mid points of the two sides through it are $( - 1, 1 )$ and $( 2, 3 )$ . Then the centroid of this triangle is:

Step-by-step solution

Let co-ordinates of $B = \left({x}_{1}, {y}_{1}\right)$
$∴ \dfrac{{x}_{1} + 1}{2} = - 1 \text{ and } \dfrac{{y}_{1} + 2}{2} = 1$
$⇒ {x}_{1} = - 3, {y}_{1} = 0$
$∴ B = ( - 3, 0 )$
Let co-ordinates of $C = \left({x}_{2}, {y}_{2}\right)$
$∴ \dfrac{{x}_{2} + 1}{2} = 2 \text{ and } \dfrac{{y}_{2} + 2}{2} = 3$
$∴ C = \left(3, 4\right)$
Let centroid $G = \left(h, k\right)$
$h = \dfrac{1 + {x}_{1} + {x}_{2}}{3} = \dfrac{1 - 3 + 3}{3} = \dfrac{1}{3}$
$k = \dfrac{2 + {y}_{1} + {y}_{2}}{3} = \dfrac{2 + 0 + 4}{3} = 2$
$∴$ Centroid, G = \left(\dfrac{1}{3}, 2\right)