A triangle has corners at #(4, 8 )#, ( 9, -2)#, and #( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

Violet Aldrich

#(5,-5/3).#

The centroid of the given triangle is #((4+9+2)/3, (8-2-1)/3) = (5,5/3).#

Now, a pt.#(a,b)# is reflected in X-axis, its reflection will be the pt.#(a,-b)#.

Hence, new co-ordinates of the reflected centroid will be #(5,-5/3).#

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Answer 2

Aurora Ayala

To find the centroid of a triangle after reflecting it across the x-axis, you need to calculate the average of the x-coordinates of the original vertices, while keeping the y-coordinate signs opposite.

Original coordinates: Vertex 1: (4, 8) Vertex 2: (9, -2) Vertex 3: (2, -1)

Reflected coordinates: Vertex 1': (4, -8) Vertex 2': (9, 2) Vertex 3': (2, 1)

Centroid formula: Centroid = ((x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3)

Calculating the new centroid: x-coordinate = (4 + 9 + 2) / 3 = 15 / 3 = 5 y-coordinate = (-8 + 2 + 1) / 3 = -5 / 3

So, the new centroid coordinates after reflecting across the x-axis are (5, -5/3).

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Answer from HIX Tutor

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