Let $A(4, 2), B(6, 5)$ and $C(1, 4)$ be the vertices of $\Delta ABC$. Find the coordinates of the centroid of the triangle.
(N/A) The coordinates of the centroid of a triangle with vertices $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ are given by the formula:
Centroid $= \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$
Given vertices are $A(4, 2), B(6, 5),$ and $C(1, 4)$.
Here,$x_1 = 4, y_1 = 2, x_2 = 6, y_2 = 5, x_3 = 1, y_3 = 4$.
Substituting these values into the formula:
Centroid $= \left( \frac{4 + 6 + 1}{3}, \frac{2 + 5 + 4}{3} \right)$
$= \left( \frac{11}{3}, \frac{11}{3} \right)$
Thus,the coordinates of the centroid are $\left( \frac{11}{3}, \frac{11}{3} \right)$.
Centroid $= \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$
Given vertices are $A(4, 2), B(6, 5),$ and $C(1, 4)$.
Here,$x_1 = 4, y_1 = 2, x_2 = 6, y_2 = 5, x_3 = 1, y_3 = 4$.
Substituting these values into the formula:
Centroid $= \left( \frac{4 + 6 + 1}{3}, \frac{2 + 5 + 4}{3} \right)$
$= \left( \frac{11}{3}, \frac{11}{3} \right)$
Thus,the coordinates of the centroid are $\left( \frac{11}{3}, \frac{11}{3} \right)$.
Explore More
Similar Questions
Find the ratio in which the $y$-axis divides the line segment joining the points $(5, -6)$ and $(-1, -4)$. Also,find the point of intersection.
Medium
View SolutionTo conduct Sports Day activities,in your rectangular shaped school ground $ABCD,$ lines have been drawn with chalk powder at a distance of $1 \,m$ each. $100$ flower pots have been placed at a distance of $1 \,m$ from each other along $AD,$ as shown in the figure. Niharika runs $\frac{1}{4}$ th the distance $AD$ on the $2^{nd}$ line and posts a green flag. Preet runs $\frac{1}{5}$ th the distance $AD$ on the $8^{th}$ line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags,where should she post her flag?
Difficult
View SolutionShow that the points $(1,7), (4,2), (-1,-1)$ and $(-4,4)$ are the vertices of a square.
Easy
View SolutionFind the values of $y$ for which the distance between the points $P(2, -3)$ and $Q(10, y)$ is $10$ units.
Medium
View SolutionFind the coordinates of a point $A,$ where $AB$ is the diameter of a circle whose centre is $(2,-3)$ and $B$ is $(1,4).$
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo