An application window on a computer screen has its corners a

An application window on a computer screen has its corners at the points A(45, 60), B(455, 60), C(45, 540), D(455, 540). A mouse move shifts the window into a new location, point A now sits at A\' (120, 120). (a) Find the translation vector t which describes the shift. (b) Find the location of the corners B, C, D after the shift. (c) Find the location of the center M of the application window before and after the shift.

Solution

Let vector be : (45 , 60) ----> ( 120,120)

x +t = 120 ; 45 +t = 120 ; t = 75

x\' = x+ 75

y +t = 120 ; 60 +t = 120 ; t = 60

y\' = y +60

t = < 75 , 60>

B(455, 60), ----> B\' =( 455+75 , 60+60) = (530, 120)

C(45, 540),----> C\' = (45+75 , 540 +60) = ( 120,600)

D(455, 540) ----> ( 455+75, 540 +60) = ( 530 , 600)

Centre , M = (250,300) ----> ( 250 +75 , 60+ 300) = ( 325 , 360)