Question

sequence of transformations
answer all parts of the question on the graph to the right. plot the pre - image and label it appropriately. make sure to show the transformations using different colors and labeling them appropriately. show the line of reflection when reflecting.

• plot the pre - image, quadrilateral opqr: o(1, - 6), p(3, - 5), q(7, - 1), r(5, - 2).
• then, translate the quadrilateral (x,y)→(x - 6,y + 7) creating image opqr.
• then, rotate opqr 180° clockwise about the origin to create image opqr

Explanation:

Step1: Perform translation

For point O(1, - 6):
$x'=1 - 6=-5$, $y'=-6 + 7 = 1$, so O' is (-5,1)
For point P(3, - 5):
$x'=3 - 6=-3$, $y'=-5 + 7 = 2$, so P' is (-3,2)
For point Q(7, - 1):
$x'=7 - 6 = 1$, $y'=-1+7 = 6$, so Q' is (1,6)
For point R(5, - 2):
$x'=5 - 6=-1$, $y'=-2 + 7 = 5$, so R' is (-1,5)

Step2: Perform 180 - degree clockwise rotation about the origin

The rule for a 180 - degree clockwise rotation about the origin is $(x,y)\to(-x,-y)$
For O'(-5,1):
O'' is (5,-1)
For P'(-3,2):
P'' is (3,-2)
For Q'(1,6):
Q'' is (-1,-6)
For R'(-1,5):
R'' is (1,-5)

Answer:

The coordinates of O'P'Q'R' are O'(-5,1), P'(-3,2), Q'(1,6), R'(-1,5) and the coordinates of O''P''Q''R'' are O''(5,-1), P''(3,-2), Q''(-1,-6), R''(1,-5)