Question

Unit test: line and triangle relationships - part 1

question 8

What are the coordinates of the centroid of a triangle with vertices P(−4, −1), Q(2, 2), and R(2, −3)?




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Answer 1

`G(0, -(2)/(3))`

Explanation:

Given that:

The coordinates of the vertices of a triangle
`\triangle PQR` are given as:

`P(-4, -1)`,
`Q(2, 2)`, and
`R(2, - 3)`.

To find:

The coordinates of the centroid of the triangle.

Solution:

The coordinates of the centroid of a triangle is given as:

`G((x_1+x_2+x_3)/(3), (y_1+y_2+y_3)/(3))`

Where
`(x_1,y_1), (x_2,y_2)\ and\ (x_3,y_3)` are the coordinates of the vertices of the triangle.

As per the given values, we have:

`x_1 = -4\\y_1 = -1\\x_2 = 2\\y_2 = 2\\x_3 = 2\\y_3 = -3`

Putting the values,we can find the coordinates of centroid as:

`G((-4+2+2)/(3), (-1+2-3)/(3))\\\Rightarrow G(0, -(2)/(3))`

Therefore, the coordinates of the centroid is:

`G(0, -(2)/(3))`