A line segment has endpoints at $(9 ,7 )$ and $(5 ,4 )$ . The line segment is dilated by a factor of $3$ around $(4 ,3 )$ . What are the new endpoints and length of the line segment?

Question

1395 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-10T09:17:40

New end points $A'((5),(4)), B' ((1),(1))$

Length of line segment $vec(A'B') = color(green)(5)$

Given $A ((9),(7)), B ((5),(4)), C ((4),(3))$ & dilation factor 3

$vec(A'C) = 4 * vec(AC)$

$A' ((x-4),(y-3)) = 3 * ((9-4),(7-3))=> ((5),(4))$

$A' ((9),(7))$

$vec(B'C) = 4 * vec(BC)$

$B' ((x-4),(y-3)) = 3 * ((5-4),4-3))=> ((1),(1))$

$B' ((5),(4))$

Length of line segment $vec(A'B') = sqrt((5-1)^2 + (4-1)^2) = color(green)(5)$

A line segment has endpoints at (9 ,7 )(9 ,7 ) and (5 ,4 )(5 ,4 ). The line segment is dilated by a factor of 3 3 around (4 ,3 )(4 ,3 ). What are the new endpoints and length of the line segment?