ABC is a triangle,G is the centroid,and D is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The centroid $G$ of a triangle $ABC$ divides the median $AD$ in the ratio $2:1$.Let $A = (2, 3)$,$G = (7, 5)$,and $D = (x, y)$.Using the section f

Vedclass · Accepted Answer

$\left(\frac{19}{2}, 6\right)$

Vedclass · Answer

(B) The centroid $G$ of a triangle $ABC$ divides the median $AD$ in the ratio $2:1$.Let $A = (2, 3)$,$G = (7, 5)$,and $D = (x, y)$.Using the section formula,the coordinates of $G$ are given by:$G = \left(\frac{2 \cdot x + 1 \cdot 2}{2+1}, \frac{2 \cdot y + 1 \cdot 3}{2+1}\right)$Equating the coordinates:$7 = \frac{2x + 2}{3}$ $\Rightarrow 21 = 2x + 2$ $\Rightarrow 2x = 19$ $\Rightarrow x = \frac{19}{2}$$5 = \frac{2y + 3}{3}$ $\Rightarrow 15 = 2y + 3$ $\Rightarrow 2y = 12$ $\Rightarrow y = 6$Therefore,the coordinates of point $D$ are $\left(\frac{19}{2}, 6\right)$.

$ABC$ is a triangle,$G$ is the centroid,and $D$ is the mid-point of $BC$. If $A = (2, 3)$ and $G = (7, 5)$,then the point $D$ is

Similar Questions

If $(0, 0)$,$(6, 0)$,and $(6, 8)$ are the vertices of a triangle,what is its incentre?

The equation of the line joining the centroid with the orthocentre of the triangle formed by the points $(-2, 3), (2, -1), (4, 0)$ is

The orthocentre of the triangle with vertices $\left( 2, \frac{\sqrt{3} - 1}{2} \right)$,$\left( \frac{1}{2}, -\frac{1}{2} \right)$,and $\left( 2, -\frac{1}{2} \right)$ is:

If two vertices of a triangle are $(5, -1)$ and $(-2, 3)$ and its orthocenter is at $(0, 0)$,find the third vertex.

The vertices of a triangle are $A(4, -2)$,$B(2, 3)$,and $C(5, -4)$. Find the equation of the median drawn from $C$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module