Question

A triangle with vertices D, E, and F are plotted on the coordinate plane at (0, 5). (2, 0), and (-4, 2), respectively. When constructed,

medians DG and EH intersect at the point with which coordinates? Round each coordinate to the nearest tenth if necessary.


A. (-0.7, 2.5)

B. (-1, 1)

C. (-0.7, 2.3)

D. (-2, 3.5)

Answer 1

Given:

Vertices of a triangle are D(0,5), E(2,0) and F(-4,2).

To find:

The intersection point of medians DG and EH.

Solution:

We know that, intersection point of all the medians of a triangle is called centroid.

The formula of centroid is

`Centroid=\left((x_1+x_2+x_3)/(3),(y_1+y_2+y_3)/(3)\right)`

Vertices of a triangle are D(0,5), E(2,0) and F(-4,2). So, the centroid of the triangle is

`Centroid=\left((0+2+(-4))/(3),(5+0+2)/(3)\right)`

`Centroid=\left((-2)/(3),(7)/(3)\right)`

`Centroid=\left(-0.666...,2.333\right)`

Round each coordinate to the nearest tenth.

`Centroid=\left(-0.7,2.3\right)`

Therefore, the correct option is C.