The mid points of $A B, B C, C A$ of a $△ A B C$ are $(6, - 1), (- 4, - 3), (2, - 5)$ respectively. The centroid of $△ A B C$

(4, 1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(\frac{4}{3}, - 3)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(\frac{4}{3}, 3)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(- \frac{4}{3}, 3)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $(\frac{4}{3}, - 3)$
The centroid formed by $Δ A B C$ is same as the centroid formed by the triangle formed by joining their midpoints.
i.e., centroid of $Δ A B C =$ centroid of $Δ P Q R$
Centroid of $Δ P Q R = (\frac{6 - 4 + 2}{3}, \frac{- 1 - 5 - 3}{3})$
$= (\frac{4}{3}, - 3)$
$∴$ Centroid of $Δ A B C = (\frac{4}{3}, - 3)$ .

Suggest Corrections

Similar questions

Q. The coordinates of the mid-points of sides AB, BC and CA of △ABC are D(1, 2, −3), E(3, 0,1) and F(−1, 1, −4) respectively. Write the coordinates of its centroid.

Q. If D, E, F are the mid-points of sides BC, CA and AB respectively of ∆ABC, then the ratio of the areas of triangles DEF and ABC is

(a) 1 : 4
(b) 1 : 2
(c) 2 : 3
(d) 4 : 5

D, E and F are respectively the mid-points of the sides BC, CA and AB of a $△$ ABC. Show that
(i) BDEF is a parallelogram.(ii) ar ( $△$ DEF) = $\frac{1}{4}$ ar ( $△$ ABC). [4 MARKS]

Q. Question 5 (ii)
D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC Show that:
(ii)

a r e a (D E F) = \frac{1}{4} a r e a (A B C)

Q. If G is the centroid of

△ A B C

and BC = 3, CA = 4, AB = 5 then BG =

Join BYJU'S Learning Program

The mid points of AB,BC,CA of a △ABC are (6,−1),(−4,−3),(2,−5) respectively. The centroid of △ABC

The correct option is B (43,−3)The centroid formed by ΔABC is same as the centroid formed by the triangle formed by joining their midpoints.i.e., centroid of ΔABC=centroid of ΔPQRCentroid of ΔPQR=(6−4+23,−1−5−33)=(43,−3)∴ Centroid of ΔABC=(43,−3).

The mid points of $A B, B C, C A$ of a $△ A B C$ are $(6, - 1), (- 4, - 3), (2, - 5)$ respectively. The centroid of $△ A B C$