A triangle has corners at $(2, 1)$ $(2, 1 )$ , $(1, 3)$ $( 1, 3 )$ , and $(5, 5)$ $(5 , 5 )$ . If the triangle is dilated by $3 x$ $3 x$ around $(1, 6)$ $(1, 6)$ , what will the new coordinates of its corners be?

Question

A triangle has corners at $(2, 1)$ $(2, 1 )$ , $(1, 3)$ $( 1, 3 )$ , and $(5, 5)$ $(5 , 5 )$ . If the triangle is dilated by $3 x$ $3 x$ around $(1, 6)$ $(1, 6)$ , what will the new coordinates of its corners be?

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Answer 1 · 2017-05-10T16:47:16

$(2, 1) \to (4, - 9)$ $(2,1)to(4,-9)$
$(1, 3) \to (1, - 3)$ $(1,3)to(1,-3)$
$(5, 5) \to (13, 3)$ $(5,5)to(13,3)$

Explanation:

The vector equation of a line from $(1, 6)$ $(1, 6)$ to $(2, 1)$ $(2,1)$ is:

$(x, y) = (1, 6) + t ((2 - 1) ˆ i + (1 - 6) ˆ j)$ $(x,y)=(1,6)+t((2-1)hati+(1-6)hatj)$

Perform the subtraction within the vector:

$(x, y) = (1, 6) + t (ˆ i - 5 ˆ j) [1]$ $(x,y)=(1,6)+t(hati-5hatj)" [1]"$

The vector equation of a line from $(1, 6)$ $(1, 6)$ to $(1, 3)$ $(1,3)$ is:

$(x, y) = (1, 6) + t ((1 - 1) ˆ i + (3 - 6) ˆ j)$ $(x,y)=(1,6)+t((1-1)hati+(3-6)hatj)$

Perform the subtraction within the vector:

$(x, y) = (1, 6) + t (- 3 ˆ j) [2]$ $(x,y)=(1,6)+t(-3hatj)" [2]"$

The vector equation of a line from $(1, 6)$ $(1, 6)$ to $(5, 5)$ $(5,5)$ is:

$(x, y) = (1, 6) + t ((5 - 1) ˆ i + (5 - 6) ˆ j)$ $(x,y)=(1,6)+t((5-1)hati+(5-6)hatj)$

Perform the subtraction within the vector:

$(x, y) = (1, 6) + t (4 ˆ i - ˆ j) [3]$ $(x,y)=(1,6)+t(4hati-hatj)" [3]"$

Here are the 3 vector equations:

$(x, y) = (1, 6) + t (ˆ i - 5 ˆ j) [1]$ $(x,y)=(1,6)+t(hati-5hatj)" [1]"$
$(x, y) = (1, 6) + t (- 3 ˆ j) [2]$ $(x,y)=(1,6)+t(-3hatj)" [2]"$
$(x, y) = (1, 6) + t (4 ˆ i - ˆ j) [3]$ $(x,y)=(1,6)+t(4hati-hatj)" [3]"$

To obtain the new points, evaluate equations [1], [2], and [3] at t = 3

$(x, y) = (1, 6) + 3 (ˆ i - 5 ˆ j)$ $(x,y)=(1,6)+3(hati-5hatj)$
$(x, y) = (1, 6) + 3 (- 3 ˆ j)$ $(x,y)=(1,6)+3(-3hatj)$
$(x, y) = (1, 6) + 3 (4 ˆ i - ˆ j)$ $(x,y)=(1,6)+3(4hati-hatj)$

$(x, y) = (4, - 9)$ $(x,y)=(4,-9)$
$(x, y) = (1, - 3)$ $(x,y)=(1,-3)$
$(x, y) = (13, 3)$ $(x,y)=(13,3)$

Answer 2 · 2017-05-10T17:04:00

$(4, - 9), (1, - 3), (13, 3)$ $(4,-9),(1,-3),(13,3)$

Explanation:

$let A = (2, 1), B = (1, 3), C = (5, 5) and D = (1, 6)$ $"let " A=(2,1),B=(1,3),C=(5,5)" and " D=(1,6)$

$"and " A',B',C'" be the images of A,B" and "C$
$"under the dilatation"$

$vec(DA)=ula-uld=((2),(1))-((1),(6))=((1),(-5))$

$rArrvec(DA')=3((1),(-5))=((3),(-15))$

$rArrA'=(1+3,6-15)=(4,-9)$
$color(blue)"--------------------------------------------------"$

$vec(DB)=ulb-uld=((1),(3))-((1),(6))=((0),(-3))$

$rArrvec(DB')=3((0),(-3))=((0),(-9))$

$rArrB'=(1+0,6-9)=(1,-3)$
$color(blue)"--------------------------------------------------"$

$vec(DC)=ulc-uld=((5),(5))-((1),(6))=((4),(-1))$

$rArrvec(DC')=3((4),(-1))=((12),(-3))$

$rArrC'=(1+12,6-3)=(13,3)$
$color(blue)"-------------------------------------------------"$

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A triangle has corners at $(2, 1)$ $(2, 1 )$ , $(1, 3)$ $( 1, 3 )$ , and $(5, 5)$ $(5 , 5 )$ . If the triangle is dilated by $3 x$ $3 x$ around $(1, 6)$ $(1, 6)$ , what will the new coordinates of its corners be?

2 Answers

Explanation:

Explanation:

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A triangle has corners at (2, 1 )(2,1)(2, 1 ), ( 1, 3 )(1,3)( 1, 3 ), and (5 , 5 )(5,5)(5 , 5 ). If the triangle is dilated by 3 x3x 3 x around (1, 6)(1,6)(1, 6), what will the new coordinates of its corners be?

2 Answers

Explanation:

Explanation:

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A triangle has corners at $(2, 1)$ $(2, 1 )$ , $(1, 3)$ $( 1, 3 )$ , and $(5, 5)$ $(5 , 5 )$ . If the triangle is dilated by $3 x$ $3 x$ around $(1, 6)$ $(1, 6)$ , what will the new coordinates of its corners be?