# A triangle has corners at #(4, 4 )#, ( 3, -2)#, and #( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

New centroid is

When triangle is reflected across the x-axis, its centroid too is reflected across the x-axis

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The centroid of a triangle remains the same after reflection across the x-axis. So, the new centroid will have the same coordinates as the original centroid. The centroid of a triangle is the average of its three vertices' coordinates. Therefore, you can find the centroid by averaging the x-coordinates and y-coordinates separately. For this triangle, the original centroid's coordinates are:

(X_{\text{centroid}} = \frac{4 + 3 + 2}{3} = 3) (Y_{\text{centroid}} = \frac{4 - 2 - 1}{3} = \frac{1}{3})

After reflection across the x-axis, the y-coordinate of each vertex is negated. So, the new centroid's coordinates are:

(X_{\text{new centroid}} = 3) (unchanged) (Y_{\text{new centroid}} = -\frac{1}{3})

Therefore, the new centroid is at (3, -1/3).

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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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