Question

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: Calculate translation coordinates

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: Calculate rotation coordinates

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:

Pre - image points: O(1, - 6), P(3, - 5), Q(7, - 1), R(5, - 2)
Translated points (O'P'Q'R'): O'(-5, 1), P'(-3, 2), Q'(1, 6), R'(-1, 5)
Rotated points (O''P''Q''R''): O''(5, - 1), P''(3, - 2), Q''(-1, - 6), R''(1, - 5)