Question

Unit test: line and triangle relationships - part 1

Answer 1

Answer:

$G(0, -\dfrac{2}{3})$

Step-by-step 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:

$G(\dfrac{x_1+x_2+x_3}{3}, \dfrac{y_1+y_2+y_3}{3})$

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:

$G(\dfrac{-4+2+2}{3}, \dfrac{-1+2-3}{3})\\\Rightarrow G(0, -\dfrac{2}{3})$

Therefore, the coordinates of the centroid is:

$G(0, -\dfrac{2}{3})$