A triangle has corners at #(6, 4 )#, ( 5, -3)#, and #( 2, -5)#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

#(13/3,4/3)#

To begin with we require to find the coordinates of the existing centroid. This is just the average of the x and y-coordinates of the 3 vertices.

#rArrx_C=1/3(6+5+2)=13/3#

and #y_C=1/3(4-3-5)=-4/3#

#rArr"coordinates of centroid" =(13/3,-4/3)#

#color(blue)"Under a reflection in the x-axis"#

a point (x ,y) → (x ,-y)

#rArr(13/3,-4/3)to(13/3,4/3)" is the new centroid"#

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Answer 2

Aurora Ayala

After reflecting the triangle across the x-axis, the new coordinates of each point will have the same x-coordinate but the y-coordinate will change sign. To find the new centroid, you would average the x-coordinates and y-coordinates separately for the three vertices of the triangle.

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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.