A triangle has corners at $(4, 5 )$ , $( 4, 3 )$ , and $( 4 , 2 )$ . If the triangle is dilated by $2 x$ around $(1, 0)$ , what will the new coordinates of its corners be?

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Answer 1 · 2018-02-12T12:00:55

New coordinates of the corners are $color(blue)(A' (7,10), color(blue)(B' (7,6),color(blue)(C' (7,4)$

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Given : A (4,5), B (4,3), C(4,2)

Dilated about D(1,0) and dilation factor 2

To find the new coordinates of the corners

$vec(A'D) = 2 * vec(AD)$

$a' - d = 2(a - d)$ or $a' = 2a - d$

$=> 2((4),(5)) - ((1),(0)) = ((7),(10))$

$color(blue)(A' (7,10)$

$vec(B'D) = 2 * vec(BD)$

$b' - d = 2(b - d)$ or $b' = 2b - d$

$=> 2((4),(3)) - ((1),(0)) = ((7),(6))$

$color(blue)(B' (7,6)$

$vec(C'D) = 2 * vec(CD)$

$c' - d = 2(c - d)$ or $c' =2c - d$

$=> 2((4),(2)) - ((1),(0)) = ((7),(4))$

$color(blue)(C' (7,4)$

A triangle has corners at (4, 5 )(4, 5 ), ( 4, 3 )( 4, 3 ), and ( 4 , 2 )( 4 , 2 ). If the triangle is dilated by 2 x 2 x around (1, 0)(1, 0), what will the new coordinates of its corners be?