Question

The vertices of a triangle are at (5,6), (2, -1) and (-1, 1). The distance between the centroid of the triangle and (5, 6) is​

Answer 1

SOLUTION

GIVEN

The vertices of a triangle are at (5,6), (2, -1) and (-1, 1).

TO DETERMINE

The distance between the centroid of the triangle and (5, 6)

EVALUATION

Here it is given that the vertices of a triangle are at (5,6), (2, -1) and (-1, 1).

Now the centroid of the triangle

$\displaystyle\sf{ = \bigg( \frac{x_1 + x_2 + x_3}{3} , \frac{y_1 + y_2 + y_3}{3} \bigg)}$

$\displaystyle\sf{ = \bigg( \frac{5 + 2 - 1}{3} , \frac{6 - 1 + 1}{3} \bigg)}$

$\displaystyle\sf{ = \bigg( \frac{6}{3} , \frac{6 }{3} \bigg)}$

$\displaystyle\sf{ = ( 2 , 2 )}$

Hence the required distance between the centroid of the triangle and (5, 6)

= The distance between (2,2) & (5,6)

$\sf{ = \sqrt{ {(5 - 2)}^{2} + {(6 - 2)}^{2} } }$

$\sf{ = \sqrt{ {(3)}^{2} + {(4)}^{2} } }$

$\sf{ = \sqrt{ 9 + 16 } }$

$\sf{ = \sqrt{ 25} }$

$\sf{ =5}$

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