Different types of questions are given under the worksheet on centroid of a triangle.
Let us recall the formula for finding the centroid of a triangle as follows;
The co-ordinates of the centroid of the triangle formed by joining the points (x₁, y₁) , (x₂, y₂) and (x₃, y₃) are
({x₁ + x₂ + x₃}/3 , {y₁ + y₂ + y₃}/3
To learn more about how to find the centroid of a triangle Click Here.
Here two varieties of questions are given:
(i) using the formula to find the centroid of a triangle where three vertices are given
(ii) for finding the third vertex where centroid of a triangle is given along with the co-ordinates of its two vertices
1. Find the co-ordinates of the centroid of the triangle formed by the following sets of three points:
(i) (7, 5), (- 2, 5) and (4, 6)
(ii) (4, - 1), (0, 3) and (- 4, - 2)
(iii) (3, - 4), (4, 7) and (2, 9) .
2. Show that the origin is the centroid of the triangle formed by the points (x - y, y - z),(- x, - y) and (y, z).
3. Find the co-ordinates of the point of intersection of the medians of the triangle formed by joining the points (-1, - 2), (8, 4) and (5, 7).
4. The co-ordinates of the vertices of a triangle are (4, - 3), (- 5, 2) and (x, y). If the centre of gravity of the triangle is at the origin find x, y.
5. The centroid of a triangle is (- 1, - 2) and co-ordinates of its two vertices are (4, 6) and (- 8, - 12). Find the co-ordinates of its third vertex.
6. The co-ordinates of the vertex A of the ∆ ABC are (2, 5); if the centroid of the triangle is at (-2, 1), find the co-ordinates of the mid-point of the side BC.
Answers for the worksheet on centroid of a triangle are given below to check the exact answers of the above questions on mid-point.
1. (i) (3, 2)
(ii) (0, 0)
( iii) (3, 4)
3. (4, 3)
4. x = 1 , y = 1
5. (1, 0)
6. (-4, -1)
● Co-ordinate Geometry
11 and 12 Grade Math
From Worksheet on Centroid of a Triangle to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Jun 13, 24 02:51 AM
Jun 13, 24 02:28 AM
Jun 13, 24 12:11 AM
Jun 12, 24 01:11 PM
Jun 11, 24 07:15 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.