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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 :

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

[tex]Centroid=\left(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\right)[/tex]

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

[tex]Centroid=\left(\dfrac{0+2+(-4)}{3},\dfrac{5+0+2}{3}\right)[/tex]

[tex]Centroid=\left(\dfrac{-2}{3},\dfrac{7}{3}\right)[/tex]

[tex]Centroid=\left(-0.666...,2.333\right)[/tex]

Round each coordinate to the nearest tenth.

[tex]Centroid=\left(-0.7,2.3\right)[/tex]

Therefore, the correct option is C.

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