A triangle has corners at $(2, 7 )$ , $( 6, 3 )$ , and $( 2 , 5 )$ . If the triangle is dilated by $2 x$ around $(2, 5)$ , what will the new coordinates of its corners be?

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A triangle has corners at $(2, 7 )$ , $( 6, 3 )$ , and $( 2 , 5 )$ . If the triangle is dilated by $2 x$ around $(2, 5)$ , what will the new coordinates of its corners be?

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Answer 1 · 2016-10-11T03:20:17

$(2,5),(10,1),(2,9)$

Explanation:

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$ABC$ is the original triangle. $AB'C'$ is the dilated triangle.

Given: $A(2,5), B(6,3), C(2,7)$

1) Given the 2X dilation is around Pt $A(2,5), A's$ coordinates remain unchanged at $(2,5)$

2) From Pt $A(2,5)$ to Pt $B(6,3)$
$Delta x = x_2-x_1=6-2=4$
$Delta y=y_2-y_1=3-5=-2$
Given scaling factor $=2X, => AB'=2AB$
$=> 2Deltax=2*4=8$ ,
$=>2Deltay=2*(-2)=-4$

$=>$ coordinates of $B'=(2+8, 5-4)=(10,1)$

3) From Pt $A(2,5)$ to Pt $C(2,7)$
$Delta x = x_2-x_1=2-2=0$ (vertical line)
$Delta y=y_2-y_1=7-5=2$
Given scaling factor $=2X, => AC'=2AC$
$=> 2Deltax=2*0=0$ ,
$=>2Deltay=2*2=4$

$=>$ coordinates of $C'=(2+0, 5+4)=(2,9)$

Hence, the new coordinates of the dilated triangle will be:
$A(2,5), B'(10,1), C'(2,9)$

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A triangle has corners at $(2, 7 )$ , $( 6, 3 )$ , and $( 2 , 5 )$ . If the triangle is dilated by $2 x$ around $(2, 5)$ , what will the new coordinates of its corners be?

1 Answer

Explanation:

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A triangle has corners at (2, 7 )(2, 7 ), ( 6, 3 )( 6, 3 ), and ( 2 , 5 )( 2 , 5 ). If the triangle is dilated by 2 x 2 x around (2, 5)(2, 5), what will the new coordinates of its corners be?

1 Answer

Explanation:

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A triangle has corners at $(2, 7 )$ , $( 6, 3 )$ , and $( 2 , 5 )$ . If the triangle is dilated by $2 x$ around $(2, 5)$ , what will the new coordinates of its corners be?