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The centroid of the triangle whose two vertices are (1,5,-2)and (3,2,7)is (-1,2,3).find the co-ordinate of third vertex?
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The centroid of the triangle whose two vertices are (1,5,-2)and (3,2,7...
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The centroid of the triangle whose two vertices are (1,5,-2)and (3,2,7...
Given Information:


- Two vertices of the triangle are (1, 5, -2) and (3, 2, 7).
- Centroid of the triangle is (-1, 2, 3).

Using the Centroid Formula:


The centroid of a triangle can be found using the following formula:

centroid = (vertex1 + vertex2 + vertex3) / 3

Step-by-Step Solution:


Step 1: Find the Coordinates of the Third Vertex:


Let the coordinates of the third vertex be (x, y, z).

Using the centroid formula, we can write the following equation:

(-1, 2, 3) = [(1, 5, -2) + (3, 2, 7) + (x, y, z)] / 3

Multiplying both sides by 3, we get:

(-3, 6, 9) = (1, 5, -2) + (3, 2, 7) + (x, y, z)

Adding the vectors on the right-hand side, we have:

(-3, 6, 9) = (4 + x, 7 + y, 5 + z)

Equating the corresponding components, we get the following equations:

-3 = 4 + x --> x = -7
6 = 7 + y --> y = -1
9 = 5 + z --> z = 4

Therefore, the coordinates of the third vertex are (-7, -1, 4).

Conclusion:


The coordinates of the third vertex of the triangle are (-7, -1, 4).
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The centroid of the triangle whose two vertices are (1,5,-2)and (3,2,7)is (-1,2,3).find the co-ordinate of third vertex?
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