enter the ordered pair corresponding to a 180 degree counterclockwise rotation of the point (-6,-11) about the point (2,3) followed by a reflection in the line x=-4 followed by a translation using the rule (x,y)- (x+8, y-1)

Question

enter the ordered pair corresponding to a 180 degree counterclockwise rotation of the point (-6,-11) about the point (2,3) followed by a reflection in the line x=-4 followed by a translation using the rule (x,y)-> (x+8, y-1)

mary1999 · Answer

Help Please

jakesaurus1127 · Answer

(-6,-11) is 8 units to the left and 9 units down of (2,3). To rotate it 180 degrees, simply switch left and right, and up and down.

mary1999 · Answer

that kinda confused me

mathmate · Answer

@mary1999
You'd need to know the basic transformations of points, such as translation, rotation, and reflection before you can handle the compound transformations.

Recall:
Translation:
T(x,y)->(x+dx,y+dy)  where (dx,dy) is the translation vector
Rotation about the $origin$.  (note: angles of rotation are clockwise)
$R_0(x,y)->(x,y)$
$R_{90}(x,y)->(-y,x)$
$R_0(x,y)->(-x,-y)$
$R_0(x,y)->(y,-x)$
Reflection about the vertical (y-) axis
$s_y(x,y)->(-x,y)$
Reflection about the horizontal  (x-) axis
$s_y(x,y)->(x,-y)$

Once the basic transformations above are mastered, you will be ready to handle general compound transformations of points similar to the question.