A triangle has corners at #(-5 ,6 )#, #(2 ,-3 )#, and #(8 ,9 )#. If the triangle is dilated by a factor of #5 # about point #(-3 ,6 ), how far will its centroid move?

Answer 1

Centroid will move by #color(brown)(23.409# units

#A(-5,6), B(2,-3), C(8,9)# Dilated by 5 around #D(-3,6)#

Centroid G(x,y) = (-5/3, 4)#

#A’ = 5A - 4D = 5((-5),(6)) - 4((-3),(6)) = ((-25),(30)) - ((-12),(16)) =color(blue)( ((-13),(14))#
#B’ = 5B - 4D = 5((2),(-3)) - 4((-3),(6)) = ((10),(-15)) - ((-12),(16)) =color(blue)( ((22),(-31))#
#C’ = 5C - 4D = 5((8),(9)) - 4((-3),(6)) = ((40),(35)) - ((-12),(16)) =color(blue)( ((52),(19))#
x Coordinate of new centroid =# G(x) = (a’ + b’ + c’)_x / 3 = (-13 + 22 + 52)/3 = 61/3#
y Coordinate of new centroid =# G(y) = (a’ + b’ + c’)_y / 3 = (14 - 31 + 19)/3 = 12#
Distance moved by centroid #d = sqrt((61/3 + 5/3)^2 + (12-4)^2) = color(brown)(23.4094#
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Answer 2

The centroid of the original triangle is located at (1.67, 4). After dilation, the centroid will move to (7.17, 24). Thus, the centroid will move 19.33 units to the right and 20 units upward.

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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.

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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