The points (11,9), (2,1) and (2,-1) are the m | vedclass

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

Question

(D) Let the vertices of the triangle be $A(x_1, y_1)$,$B(x_2, y_2)$,and $C(x_3, y_3)$.Given mid-points are $F(11, 9)$,$E(2, 1)$,and $D(2, -1)$.Since t

Vedclass · Accepted Answer

$(5,3)$

Vedclass · Answer

(D) Let the vertices of the triangle be $A(x_1, y_1)$,$B(x_2, y_2)$,and $C(x_3, y_3)$.Given mid-points are $F(11, 9)$,$E(2, 1)$,and $D(2, -1)$.Since the centroid of a triangle formed by joining the mid-points of the sides of a triangle is the same as the centroid of the original triangle,we can directly calculate it.The centroid $(G)$ of the triangle with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ is given by $\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right)$.Let the mid-points be $(x_a, y_a) = (11, 9)$,$(x_b, y_b) = (2, 1)$,and $(x_c, y_c) = (2, -1)$.The centroid of the triangle formed by these mid-points is $\left(\frac{11+2+2}{3}, \frac{9+1-1}{3}\right) = \left(\frac{15}{3}, \frac{9}{3}\right) = (5, 3)$.Thus,the centroid of the original triangle is $(5, 3)$.

The points $(11,9), (2,1)$ and $(2,-1)$ are the mid-points of the sides of a triangle. Then,the centroid is

Similar Questions

The vertices of a triangle are at $-\hat{i}+3 \hat{j}$ and $2 \hat{i}+5 \hat{j}$ and its orthocenter is at $\hat{i}+2 \hat{j}$. If the position vector of the third vertex is $a \hat{i}+b \hat{j}$,then $(a, b)=$

Let $PQR$ be an acute-angled triangle in which $PQ < QR$. From the vertex $Q$,draw the altitude $QQ_1$,the angle bisector $QQ_2$,and the median $QQ_3$,with $Q_1, Q_2, Q_3$ lying on $PR$. Then,

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

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

The incentre of the triangle formed by the vertices $(0, 0)$,$(5, 12)$,and $(16, 12)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module