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 circumcentre of the triangle with vertices $A(1, 2)$,$B(-2, 2)$,and $C(1, 5)$.

Find the area of a quadrilateral having the vertices $(-1, -1), (-4, -2), (-5, -4),$ and $(-2, -3)$.

State whether the following statements are true or false. Justify your answer.
The points $(0,5), (0,-9)$ and $(3,6)$ are collinear.

Find the area of the quadrilateral whose vertices,taken in order,are $(-4,-2), (-3,-5), (3,-2),$ and $(2,3)$ (in square units).

In $\Delta ABC$,if $A(1, 7)$,$B(2, 4)$,and $C(k, 5)$ and $\angle A$ is a right angle,then find the value of $k$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module