In Delta ABC,A(1, 2),B(3, 4),and C lies on th | vedclass

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

Question

(A) Let the coordinates of $C$ be $(x, 0)$ since it lies on the $X$-axis.The coordinates of the centroid $G$ of a triangle with vertices $(x_1, y_1)$,

Vedclass · Accepted Answer

$(-4, 0)$

Vedclass · Answer

(A) Let the coordinates of $C$ be $(x, 0)$ since it lies on the $X$-axis.The coordinates of the centroid $G$ of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ are given by $(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3})$.Substituting the given values: $G = (\frac{1+3+x}{3}, \frac{2+4+0}{3}) = (\frac{4+x}{3}, 2)$.Since the centroid $G$ lies on the $Y$-axis,its $x$-coordinate must be $0$.Therefore,$\frac{4+x}{3} = 0$.$4+x = 0 \implies x = -4$.Thus,the coordinates of $C$ are $(-4, 0)$.

In $\Delta ABC$,$A(1, 2)$,$B(3, 4)$,and $C$ lies on the $X$-axis. If the centroid $G$ of $\Delta ABC$ is on the $Y$-axis,then find the coordinates of $C$.

Similar Questions

If $A(x_{1}, y_{1})$ and $B(x_{2}, y_{2})$ are the given points,then $d(A, B) = $ .........

The distance between the points $A(a+b, b-a)$ and $B(a-b, a+b)$ is............

If the vertices of $\Delta ABC$ are $A(1, 4)$,$B(-3, 2)$,and $C(5, 0)$,then the length of the median $\overline{AD}$ is.........

If the vertices of $\Delta ABC$ are $A(0, 0)$,$B(4, 0)$ and $C(0, 6)$,then the coordinates of the point $P$ which is equidistant from $A, B$ and $C$ and in the plane of $\Delta ABC$ is $\ldots \ldots \ldots$

$A(6,1), B(8,2)$ and $C(9,4)$ are three vertices of a parallelogram $ABCD$. If $E$ is the midpoint of $DC$,find the area of $\triangle ADE$ (in sq. units).

Vedclass Test Series

Exam Paper Generator

Online Exam Module