A triangle has corners at #(9 ,5 )#, #(2 ,7 )#, and #(3 ,2 )#. How far is the triangle's centroid from the origin?
The distance of centroid from the origin is
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To find the centroid of a triangle with vertices at points ( A(x_1, y_1) ), ( B(x_2, y_2) ), and ( C(x_3, y_3) ), you can use the following formulas:
[ x_c = \frac{x_1 + x_2 + x_3}{3} ] [ y_c = \frac{y_1 + y_2 + y_3}{3} ]
Given the vertices ( A(9, 5) ), ( B(2, 7) ), and ( C(3, 2) ), you can calculate the coordinates of the centroid.

Calculate ( x_c ): [ x_c = \frac{9 + 2 + 3}{3} ] [ x_c = \frac{14}{3} ]

Calculate ( y_c ): [ y_c = \frac{5 + 7 + 2}{3} ] [ y_c = \frac{14}{3} ]
The coordinates of the centroid ( G(x_c, y_c) ) are ( \left(\frac{14}{3}, \frac{14}{3}\right) ).
To find the distance from the centroid to the origin, you can use the distance formula:
[ \text{Distance} = \sqrt{(x_c  0)^2 + (y_c  0)^2} ]
Substitute the coordinates of the centroid ( G ) into this formula:
[ \text{Distance} = \sqrt{\left(\frac{14}{3}\right)^2 + \left(\frac{14}{3}\right)^2} ]
[ \text{Distance} = \sqrt{\frac{196}{9} + \frac{196}{9}} ]
[ \text{Distance} = \sqrt{\frac{392}{9}} ]
[ \text{Distance} = \frac{\sqrt{392}}{3} ]
So, the distance from the centroid of the triangle to the origin is ( \frac{\sqrt{392}}{3} ) units.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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