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A triangle has corners at #(4 ,9 )#, #(3 ,7 )#, and #(7 ,2 )#. How far is the triangle's centroid from the origin?

Answer 1

Mason Adams

Distance of centroid from origin is #color(red)(7.6)#

Coordinates of centroid #x = (x1 + x2 + x3)/3 = (4+3+7)/3 = 14/3#

#y = (y1 + y2 + y3/3 = (+7+2)/3 = 6#

Distance of centroid from origin is

#d = sqrt((14/3)^2 + (6^2)) ~~ color (red)(7.6)#

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Answer 2

Jayden Jackson

To find the centroid of a triangle with vertices at ((x_1, y_1)), ((x_2, y_2)), and ((x_3, y_3)), you can use the formula:

[ \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) ]

For the given triangle with vertices (4, 9), (3, 7), and (7, 2):

[ x_1 = 4, \quad y_1 = 9 ] [ x_2 = 3, \quad y_2 = 7 ] [ x_3 = 7, \quad y_3 = 2 ]

Plug these values into the centroid formula to find the centroid coordinates.

Then, calculate the distance between the centroid and the origin using the distance formula:

[ \sqrt{(x - 0)^2 + (y - 0)^2} ]

Where ( (x, y) ) are the coordinates of the centroid.

This will give you the distance from the centroid to the origin.

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Answer from HIX Tutor

When evaluating a one-sided 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.