A triangle has corners at $(5, 3)$ $(5 ,3 )$ , $(4, 6)$ $(4 ,6 )$ , and $(8, 5)$ $(8 ,5 )$ . If the triangle is dilated by a factor of $2$ $2$ about point $(3, 2)$ $(3 ,2 )$ , how far will its centroid move?

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A triangle has corners at $(5, 3)$ $(5 ,3 )$ , $(4, 6)$ $(4 ,6 )$ , and $(8, 5)$ $(8 ,5 )$ . If the triangle is dilated by a factor of $2$ $2$ about point $(3, 2)$ $(3 ,2 )$ , how far will its centroid move?

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Answer 1 · 2018-04-18T04:02:51

$\frac{8 \sqrt{2}}{3}$ $(8sqrt2)/3$

Explanation:

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Let $G (x_{a}, y_{a})$ $G(x_a,y_a)$ be the centroid of $DeltaABC$ , as shown in the figure,
$G(x_a,y_a)=((5+4+8)/3, (3+6+5)/3)=(17/3,14/3)$
Let $D(3,2)$ be the center of dilation.
Let $d$ be the distance between $D and G$ ,
$=> d=sqrt((17/3-3)^2+(14/3-2)^2)=(8sqrt2)/3$ units
given that the scale factor $k=2$ ,
$=>$ the centroid $G$ will move by $(k-1)xxd=(2-1)xx(8sqrt2)/3=(8sqrt2)/3$ units

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A triangle has corners at $(5, 3)$ $(5 ,3 )$ , $(4, 6)$ $(4 ,6 )$ , and $(8, 5)$ $(8 ,5 )$ . If the triangle is dilated by a factor of $2$ $2$ about point $(3, 2)$ $(3 ,2 )$ , how far will its centroid move?

1 Answer

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A triangle has corners at (5 ,3 )(5,3)(5 ,3 ), (4 ,6 )(4,6)(4 ,6 ), and (8 ,5 )(8,5)(8 ,5 ). If the triangle is dilated by a factor of 2 22 about point (3 ,2 )(3,2)(3 ,2 ), how far will its centroid move?

1 Answer

Explanation:

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A triangle has corners at $(5, 3)$ $(5 ,3 )$ , $(4, 6)$ $(4 ,6 )$ , and $(8, 5)$ $(8 ,5 )$ . If the triangle is dilated by a factor of $2$ $2$ about point $(3, 2)$ $(3 ,2 )$ , how far will its centroid move?