Name: ___________________

Date:___________________

kwizNET Subscribers, please login to turn off the Ads!
Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!

High School Mathematics - 2
9.16 Centroid of a Triangle

To find the centroid of a triangle whose vertices are given

Let A(x1, y1), B(x2, y2) and C(x3, y3) be the vertices of the triangle ABC. Let AD be the median bisecting the base.
Then D = {(x2 + x3)/2, (y2 + y3)/2}
Now the point G on AD, which divides it internally in the ratio 2:1, is the centroid. If (x,y) are the coordinates of G, then
x = 2x(x2+x3)/2 + (1 x x1)/2+1 = (x1+x2+x3)/3
y = 2x(y2+y3)/2 + (1 x y1)/(2+1) = (y1+y2+y3)/3
Hence, the coordinates of the centroid are given by
x = (x1+x2+x3)/3, y = (y1+y2+y3)/3.

Directions: Solve the following.

Name: ___________________

Date:___________________

High School Mathematics - 2
9.16 Centroid of a Triangle

Q 1: Origin is the centroid of the triangle, whose two vertices are (5, -1), (-2,3).Find the third vertex.
(3, 2)
(-3, -2)
(3,-2)

Q 2: The coordnates of the vertices of the triangle are (4, -3), (-5,2) and (x,y). If the centroid of the triangle is at the origin, what is the value of x and y.
(0,1)
0
(1,1)
1

Q 3: Find the centroid of the triangle whose angular points are (-1,0), (5, -2) and (8, -2)
(0, -4)
(0, 4)
(4, 0)
(-4,0)

Q 4: Find the centroid of the triangle whose angular points are (3, -5), (-7, 4) and (10, -2) respectively.
(-2, 1)
(2, -1)
(-2, -1)
(2, 1)

Q 5: Find the length of the median AD of a triangle whose vertices are A(4,4), B(3,-2) and C(-3,16).
7
10
5
3

Q 6: If (2,4) is the centroid of the triangle two of whose vertices are (7,1) and (2,7). Find the remaining vertex.
(-3,4)
(-3,-4)
(3,-4)
(3,4)

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


Subscription to kwizNET Learning System costs less than $1 per month & offers the following benefits:

  • Unrestricted access to grade appropriate lessons, quizzes, & printable worksheets
  • Instant scoring of online quizzes
  • Progress tracking and award certificates to keep your student motivated
  • Unlimited practice with auto-generated 'WIZ MATH' quizzes
  • Child-friendly website with no advertisements


© 2003-2007 kwizNET Learning System LLC. All rights reserved. This material may not be reproduced, displayed, modified or distributed without the express prior written permission of the copyright holder. For permission, contact info@kwizNET.com
For unlimited printable worksheets & more, go to http://www.kwizNET.com.