If the midpoints of the sides overline{AB},ov | vedclass

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

Question

(C) Let the vertices of $\Delta ABC$ be $A(x_1, y_1)$,$B(x_2, y_2)$,and $C(x_3, y_3)$.Given midpoints are $D(1, 2)$,$E(2, 1)$,and $F(3, 3)$.The centro

Vedclass · Accepted Answer

$(2, 2)$

Vedclass · Answer

(C) Let the vertices of $\Delta ABC$ be $A(x_1, y_1)$,$B(x_2, y_2)$,and $C(x_3, y_3)$.Given midpoints are $D(1, 2)$,$E(2, 1)$,and $F(3, 3)$.The centroid of $\Delta ABC$ is given by $G = (\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3})$.$A$ key property of triangles is that the centroid of the triangle formed by the midpoints of the sides is the same as the centroid of the original triangle.Thus,the centroid $G$ is the average of the coordinates of the midpoints $D, E,$ and $F$.$G = (\frac{1+2+3}{3}, \frac{2+1+3}{3}) = (\frac{6}{3}, \frac{6}{3}) = (2, 2)$.

If the midpoints of the sides $\overline{AB}$,$\overline{BC}$,and $\overline{CA}$ in $\Delta ABC$ are respectively $D(1, 2)$,$E(2, 1)$,and $F(3, 3)$,then find the centroid of $\Delta ABC$.

Similar Questions

Find the points of trisection of the line segment joining $(7, 5)$ and $(-2, -1)$.

Show that $(2,2), (5,2), (5,5)$ and $(2,5)$ are the vertices of a square.

Two vertices of a triangle are $(3, -5)$ and $(-7, 4)$. If the centroid of the triangle is $(2, -1)$,then find the coordinates of the third vertex.

The distance of point $A(a \cos \theta, a \sin \theta)$ from the origin is $\ldots \ldots \ldots \ldots$ $(a \in R^{+})$

If the vertices of $\Delta ABC$ are $A(x_{1}, y_{1})$,$B(x_{2}, y_{2})$,and $C(x_{3}, y_{3})$,then the centroid of $\Delta ABC$ is........

Vedclass Test Series

Exam Paper Generator

Online Exam Module