A triangle has corners at #(7 ,6 )#, #(4 ,4 )#, and #(6 ,7 )#. How far is the triangle's centroid from the origin?

Answer 1

The distance is #=8.01#

The 3 corners of the triangle is #(7,6)#, #(4,4)#, and #(6,7)#

The centroid is

#x_c=(7+4+6)/3=17/3#

#y_c=(6+4+7)/3=17/3#

The distance of the centroid from the origin is

#d=sqrt((17/3)^2+(17/3)^2)#

#=17/3sqrt2#

#=8.01#

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Answer 2

To find the centroid of a triangle, you average the x-coordinates and the y-coordinates of its vertices. The formula for the centroid (Cx, Cy) of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is:

Cx = (x1 + x2 + x3) / 3 Cy = (y1 + y2 + y3) / 3

Using the given coordinates: x1 = 7, y1 = 6 x2 = 4, y2 = 4 x3 = 6, y3 = 7

Cx = (7 + 4 + 6) / 3 = 17 / 3 ≈ 5.67 Cy = (6 + 4 + 7) / 3 = 17 / 3 ≈ 5.67

The centroid of the triangle is approximately (5.67, 5.67).

To find the distance between the centroid and the origin, you can use the distance formula: Distance = √((Cx - 0)^2 + (Cy - 0)^2) = √(5.67^2 + 5.67^2) ≈ √(32.1489 + 32.1489) ≈ √64.2978 ≈ 8.01

So, the distance from the centroid of the triangle to the origin is approximately 8.01 units.

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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.

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.

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.

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.

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