Assertion: If (0, 3), (1, 1) and (-1, 2) are | vedclass

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

Question

(A) Let the vertices of the triangle be $A(x_1, y_1), B(x_2, y_2)$,and $C(x_3, y_3)$.The midpoints of the sides are given as $D(0, 3), E(1, 1)$,and $F

Vedclass · Accepted Answer

$A$ and $R$ are both true and $R$ is the correct explanation of $A$.

Vedclass · Answer

(A) Let the vertices of the triangle be $A(x_1, y_1), B(x_2, y_2)$,and $C(x_3, y_3)$.The midpoints of the sides are given as $D(0, 3), E(1, 1)$,and $F(-1, 2)$.The centroid of the triangle formed by the midpoints is the same as the centroid of the original triangle.Centroid of $\Delta DEF = \left( \frac{0 + 1 - 1}{3}, \frac{3 + 1 + 2}{3} \right) = \left( \frac{0}{3}, \frac{6}{3} \right) = (0, 2)$.Since the centroid of the triangle formed by the midpoints is $(0, 2)$,the centroid of the original triangle is also $(0, 2)$.Thus,both Assertion $A$ and Reason $R$ are true,and $R$ is the correct explanation of $A$.

Assertion: If $(0, 3), (1, 1)$ and $(-1, 2)$ are the midpoints of the sides of a triangle,then the centroid of the original triangle is $(0, 2)$.
Reason: The centroid of a triangle and the centroid of the triangle formed by joining the midpoints of the sides of the original triangle are the same.

Similar Questions

If $O, G, S$ are respectively the orthocentre,centroid and circumcentre of a triangle whose vertices are $A(2,3), B(2,4)$ and $C(4,3)$,then $AO^2 + 9BG^2 + 4CS^2 =$

$A$ tower stands vertically inside an acute-angled triangular park $\Delta PQR$. If the angle of elevation of the top of the tower from each corner of the park is the same,then in $\Delta PQR$,the foot of the tower is at the

If $(a, b - c)$,$(b, c - a)$,and $(c, a - b)$ are the vertices of a triangle,then where does the centroid of the triangle lie?

In a $\triangle ABC$,if the medians $AD$ and $BE$ are such that $AD=4$,$\angle DAB=\frac{\pi}{6}$ and $\angle ABE=\frac{\pi}{3}$,then the area of $\triangle ABC$ (in square units) is

In $\Delta ABC$,the coordinates of $B$ are $(0, 0)$,$AB = 2$,$\angle ABC = \frac{\pi}{3}$,and the coordinates of the midpoint of $BC$ are $(2, 0)$. Find the centroid of the triangle.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Assertion: If $(0, 3), (1, 1)$ and $(-1, 2)$ are the midpoints of the sides of a triangle,then the centroid of the original triangle is $(0, 2)$.Reason: The centroid of a triangle and the centroid of the triangle formed by joining the midpoints of the sides of the original triangle are the same.