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

The coordinates of the centroid of the triangle with vertices $(2, 3)$,$(4, 7)$,and $(-3, 2)$ are:

Find the ratio in which the point $P \left(\frac{3}{4}, \frac{5}{12}\right)$ divides the line segment joining the points $A \left(\frac{1}{2}, \frac{3}{2}\right)$ and $B(2, -5)$. (in $: 5$)

If $(a, b)$ is the mid-point of the line segment joining the points $A (10, -6)$ and $B (k, 4)$ and $a - 2b = 18$,find the value of $k$ and the distance $AB$.

$A$ point $(4,4)$ divides the line segment joining $A(2,6)$ and $B(6,2)$ from $A$,then the ratio of division is $\ldots \ldots \ldots \ldots .$

Obtain the circumcentre of $\Delta ABC$ with vertices $A (-3, -1)$,$B (-1, 3)$ and $C (6, 2)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module