A line segment goes from (1 ,2 )(1,2) to (4 ,1 )(4,1). The line segment is reflected across x=-3x=−3, reflected across y=1y=1, and then dilated about (2 ,2 )(2,2) by a factor of 33. How far are the new endpoints from the origin?

1 Answer
sankarankalyanam
Apr 12, 2018

color(violet)("Distance of A & B from origin after reflection and dilation " 9, 12.04 " respy."Distance of A & B from origin after reflection and dilation 9,12.04 respy.

Explanation:

A (1,2), B (4,1)," reflected across " x = -3, y = 1A(1,2),B(4,1), reflected across x=−3,y=1

"Reflection Rule : reflect thru " x = -3, y = 1, h=-3, k=1Reflection Rule : reflect thru x=−3,y=1,h=−3,k=1

A'(x,y) = A(2h-x, 2k-y) = (-6-1, 4-2) = (-7,2)

B'(x,y) = B(2h-x, 2k-y) = (-6-4, 4-1) = (-10,3)

Points A' & B' dilated about C(2,2) by a factor of 2.

A'(x,y) -> A''(x,y) = A'(x,y) - C(x,y) = ((-7,2) - (2,2)) = (-9,0)

B'(x,y) -> B''(x,y) = B'(x,y) - C(x,y) = ((-10,3) - (2,2)) = (-12,1)

OA' = 9, OB' = sqrt(-12^2 + 1^2 = 12.04

Related questions
See all questions in Reflections
Impact of this question
1768 views around the world
You can reuse this answer
Creative Commons License