Question

the distance from the origin to the centroid of the triangle whose vertices are (7,1) (1,5) and (1,6) is
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Answer 1

Answer:

5 units

Step-by-step explanation:

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Answer 2

Given:

triangle whose vertices are (7,1) (1,5) and (1,6)

To Find:

the distance from the origin to the centroid of the triangle

Solution:

A centroid is defined as the intersection of the three medians of the triangle.

A median is defined as the line joining the vertex and the midpoint in the line opposite to the vertex.

The centroid divides the median in the ratio of 1:2.

The formula for the centroid of a triangle with three vertices given will be,

$Centroid(x,y)=[\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3} ]$

Using this formula calculating the coordinates for the centroid we have,

$Centroid(x,y)=(\frac{7+1+1}{3} ,\frac{1+5+6}{3} )\\=(3,4)$

Now to find the distance of this point from the origin we will use the distance formula,

$D=\sqrt{3^2+4^2}\\=\sqrt{9+16}\\=\sqrt{25}\\=5unit$

Hence, the distance from the origin to the centroid of the triangle whose vertices are (7,1) (1,5) and (1,6) is 5 units.