Two vertices of the triangle are (3, 1) and ( | vedclass

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

Question

(B) Let the vertices of the triangle be $A(3, 1)$,$B(1, 5)$,and $C(x, y)$.The centroid $G$ of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $

Vedclass · Accepted Answer

$(-4, -6)$

Vedclass · Answer

(B) Let the vertices of the triangle be $A(3, 1)$,$B(1, 5)$,and $C(x, y)$.The centroid $G$ of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ is given by the formula $G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$.Given that the centroid $G$ is the origin $(0, 0)$,we have:$\frac{3 + 1 + x}{3} = 0 \implies 4 + x = 0 \implies x = -4$.$\frac{1 + 5 + y}{3} = 0 \implies 6 + y = 0 \implies y = -6$.Therefore,the third vertex is $(-4, -6)$.

Two vertices of the triangle are $(3, 1)$ and $(1, 5)$. If the centroid of the triangle is the origin,then the third vertex is:

Similar Questions

Find the area of the triangle whose vertices are $(-8, 4), (-6, 6)$ and $(-3, 9).$

Find the values of $k$ if the points $A(k+1, 2k)$,$B(3k, 2k+3)$ and $C(5k-1, 5k)$ are collinear.

Two vertices of a triangle are $A(2, 1)$ and $B(3, -2)$. The third vertex is $C(x, y)$,where $y = x + 3$. If the area of the triangle is $5$,find the coordinates of the third vertex.

For points $A(1, 7)$,$B(2, 4)$,and $C(k, 5)$,if $\angle A = 90^\circ$,then find the value of $k$.

If the point $P (2,1)$ lies on the line segment joining points $A (4,2)$ and $B (8,4)$,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module