Question

Use the following information; the Unit Formula Sheet, and the Desmos Calculator both to graph and compute; in answering the following questions.

Given ∆ABC; with points A(4,5); B(20,25); and C(30,6). Compute the centroid.

Express in Coordinate form, (x,y), do not input spaces.


∆ABC centroid is ___ use coordinate notation(x,y)

Answer 1

The centroid of triangle ∆ABC is (18, 12) in coordinate notation. This means that the point of intersection of the medians of the triangle is located at (18, 12).

To find the centroid of a triangle ∆ABC, we need to calculate the average of the x-coordinates and the average of the y-coordinates of its three vertices.

Given the coordinates of points A(4,5), B(20,25), and C(30,6), we can find the centroid as follows:

1. Add the x-coordinates of A, B, and C:

x = 4 + 20 + 30 = 54

2. Divide the sum by 3 to find the average:

x = 54 / 3 = 18

3. Add the y-coordinates of A, B, and C:

y = 5 + 25 + 6 = 36

4. Divide the sum by 3 to find the average:

y = 36 / 3 = 12

Therefore, the centroid of triangle ∆ABC is (18, 12) in coordinate notation. This means that the point of intersection of the medians of the triangle is located at (18, 12).