If the coordinates of the vertices of a trian | vedclass

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

Question

(C) The coordinates of the vertices are $(1, a)$,$(2, b)$,and $(c^2, 3)$.The centroid $(G)$ of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and

Vedclass · Accepted Answer

Cannot lie on the $y$-axis

Vedclass · Answer

(C) The coordinates of the vertices are $(1, a)$,$(2, b)$,and $(c^2, 3)$.The centroid $(G)$ of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ is given by $G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$.Substituting the given values,the centroid is $\left( \frac{1 + 2 + c^2}{3}, \frac{a + b + 3}{3} \right) = \left( \frac{3 + c^2}{3}, \frac{a + b + 3}{3} \right)$.For the centroid to lie on the $y$-axis,its $x$-coordinate must be zero.$\frac{3 + c^2}{3} = 0 \implies 3 + c^2 = 0 \implies c^2 = -3$.Since $c^2$ cannot be negative for any real value of $c$,the $x$-coordinate can never be zero.Therefore,the centroid cannot lie on the $y$-axis.

If the coordinates of the vertices of a triangle are $(1, a)$,$(2, b)$,and $(c^2, 3)$,then the centroid of the triangle:

Similar Questions

If the median $AD$ of the triangle $ABC$ is bisected at $E$ and $BE$ meets $AC$ in $F$,then $AF: AC=$

The orthocentre of the triangle whose vertices are $(0, 0)$,$(2, -1)$,and $(1, 3)$ is

The circumcentre of the triangle formed by the points $A(1, \sqrt{3})$,$B(-1, -\sqrt{3})$,and $C(3, -\sqrt{3})$ is

Let $PS$ be the median of the triangle with vertices $P(2,2)$,$Q(6,-1)$,and $R(7,3)$. The equation of the line passing through $(1,-1)$ and parallel to $PS$ is:

The two vertices of a triangle are $(-1, 4)$ and $(5, 2)$. If its centroid is $(0, -3)$,find the third vertex.

Vedclass Test Series

Exam Paper Generator

Online Exam Module