# A triangle has corners at #(8, 3 )#, ( 5, -8)#, and #(7, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

Then.

Here.

Under reflection in the x-axis, a point (x ,y) → (x ,-y)

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To find the centroid of the reflected triangle across the x-axis, you would need to reflect each of the original vertices across the x-axis to obtain their new coordinates. Then, you would calculate the average of the x-coordinates and the average of the y-coordinates of the new vertices to find the centroid.

For each vertex (x, y), its reflection across the x-axis would have coordinates (x, -y).

The original vertices are: A(8, 3), B(5, -8), and C(7, -4).

The reflected vertices would be: A'(8, -3), B'(5, 8), and C'(7, 4).

Now, to find the centroid, calculate the average of the x-coordinates and the average of the y-coordinates of the reflected vertices:

Average of x-coordinates: [ \frac{8 + 5 + 7}{3} = \frac{20}{3} ]

Average of y-coordinates: [ \frac{-3 + 8 + 4}{3} = \frac{9}{3} = 3 ]

Therefore, the coordinates of the centroid of the reflected triangle across the x-axis are (\left(\frac{20}{3}, 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.

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