# A triangle has corners at #(2, 7 )#, ( 5, -2)#, and #( 1, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

The new centroid

From the old centroid :(8/3, 4/3)

God bless...I hope the explanation is useful.

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To find the new centroid of the triangle after reflection across the x-axis, you need to reflect each vertex across the x-axis and then calculate the centroid of the new triangle.

The reflection of a point ((x, y)) across the x-axis becomes ((x, -y)).

So, reflecting the vertices:

- ((2, 7)) becomes ((2, -7))
- ((5, -2)) becomes ((5, 2))
- ((1, -1)) becomes ((1, 1))

Now, calculate the coordinates of the centroid of the new triangle:

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

Substitute the reflected coordinates into the formula:

[ \text{New centroid} = \left(\frac{2 + 5 + 1}{3}, \frac{-7 + 2 + 1}{3}\right) ]

[ \text{New centroid} = \left(\frac{8}{3}, \frac{-4}{3}\right) ]

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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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