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A triangle has corners at #(3, 7 )#, ( 5, -5)#, and #( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

Wyatt Anderson

New centroid is #(10/3,-1/3)#

The centroid of the triangle with corners at #(3,7)#, #(5,-5)# and #(2, -1 )# is

#((3+5+2)/3,(7+(-5)+(-1))/3)# or #(10/3,1/3)#

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

and as reflection of a point #(x_1,y_1)# in x-axis is #(x_1,-y_1)#,

New centroid is #(10/3,-1/3)#

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Answer 2

Aaliyah Anderson

The centroid of the original triangle is at (3.333, 0.333) coordinates. When the triangle is reflected across the x-axis, its new centroid will have the same x-coordinate but the y-coordinate will be negated, resulting in the new centroid at (3.333, -0.333).

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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.