If the midpoints of the sides of a triangle a | vedclass

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

Question

(C) The centroid of a triangle is the same as the centroid of the triangle formed by joining the midpoints of its sides.Let the midpoints be $(x_1, y_

Vedclass · Accepted Answer

$(2, 5/3)$

Vedclass · Answer

(C) The centroid of a triangle is the same as the centroid of the triangle formed by joining the midpoints of its sides.Let the midpoints be $(x_1, y_1) = (-2, 3)$,$(x_2, y_2) = (4, -3)$,and $(x_3, y_3) = (4, 5)$.The centroid $(G)$ is given by the formula:$G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$Substituting the values:$G = \left( \frac{-2 + 4 + 4}{3}, \frac{3 - 3 + 5}{3} \right)$$G = \left( \frac{6}{3}, \frac{5}{3} \right)$$G = \left( 2, \frac{5}{3} \right)$Thus,the correct option is $(C)$.

If the midpoints of the sides of a triangle are $(-2, 3), (4, -3)$ and $(4, 5)$,then the centroid of the triangle is

Similar Questions

In $\triangle ABC$,if $A=(1,2)$ and the equations of the medians through $B$ and $C$ are $x+y=5$ and $x=4$ respectively,then the area of $\triangle ABC$ is

Let the vertex of a triangle $ABC$ be $A(1, 2)$, and the mid-point of the side $AB$ be $M(5, -1)$. If the centroid of this triangle is $G(3, 4)$ and its circumcenter is $O(\alpha, \beta)$, then $21(\alpha + \beta)$ is equal to:

The vertices of a triangle are $A(0,0), B(0,2)$ and $C(2,0)$. Find the distance between its orthocentre and circumcentre.

The incentre of the triangle with vertices $(1, \sqrt{3}), (0, 0)$ and $(2, 0)$ is:

If the midpoints of the sides of a triangle are $(5, 0)$,$(5, 12)$,and $(0, 12)$,then what is the orthocenter of this triangle?

Vedclass Test Series

Exam Paper Generator

Online Exam Module