A triangle has corners at $(-2 ,3 )$ , $(3 ,2 )$ , and $(5 ,-6 )$ . If the triangle is dilated by a factor of $2$ about point #(1 ,-8 ), how far will its centroid move?

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A triangle has corners at $(-2 ,3 )$ , $(3 ,2 )$ , and $(5 ,-6 )$ . If the triangle is dilated by a factor of $2$ about point #(1 ,-8 ), how far will its centroid move?

1 Answer

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Answer 1 · 2016-12-06T08:40:06

$d=7.73" (shown in figure)"$

Explanation:

$"The original triangle and its centroid is shown in figure below."$

enter image source here

$"the original centroid can be calculated using:"$

$x=(-2+3+5)/3=6/3=2$

$y=(3+2+-6)/3=-1/3=-0,33$

$E(2,-0.33)$

$"Now dilate A(-2,3) by factor 2 with respect to D(1,-8)"$

enter image source here

$A(-2,3) rArr A'(1-3*2,3+11*2)$

$A'(1-3*2,-8+11*2)$

$A'(-5,14)" (shown in figure below)"$

# enter image source here #

$"Dilate B(3,2) by factor 2 with respect to D(1,-8)"$

enter image source here

$B(3,2) rArr B'(1+2*2,-8+10*2)$

$B'(1+2*2,-8+10*2)$

$B'(5,12)" (shown in figure below)"$

enter image source here

$"Dilate C(5,-6) by factor 2 with respect to D(1,-8)"$

enter image source here

$C(5,-6) rArr C'(1+4*2,-8+2*2)$

$C'(1+4*2,-8+2*2)$

$C'(9,-4)" (shown figure below)"$

enter image source here

$"Finally.."$

$"the dilated centroid can be calculated "$

$x'=(-5+5+9)/3=9/3=3$

$y'=(14+12-4)/3$

$y'=22/3=7,33$

$F(3,7.33)$

enter image source here

$"distance between E and F"$

$d=sqrt((3-2)^2+(7.33+0.33)^2)$

$d=sqrt(1+(7.66)^2)$

$d=sqrt(1+58.68)$

$d=sqrt(59.68)$

$d=7.73$

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A triangle has corners at $(-2 ,3 )$ , $(3 ,2 )$ , and $(5 ,-6 )$ . If the triangle is dilated by a factor of $2$ about point #(1 ,-8 ), how far will its centroid move?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

A triangle has corners at (-2 ,3 )(-2 ,3 ), (3 ,2 )(3 ,2 ), and (5 ,-6 )(5 ,-6 ). If the triangle is dilated by a factor of 2 2 about point #(1 ,-8 ), how far will its centroid move?

1 Answer

Explanation:

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Impact of this question

A triangle has corners at $(-2 ,3 )$ , $(3 ,2 )$ , and $(5 ,-6 )$ . If the triangle is dilated by a factor of $2$ about point #(1 ,-8 ), how far will its centroid move?