Find the best answers to your questions with the help of IDNLearn.com's knowledgeable users. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.
a) The points of the new quadrillateral are [tex]A'(x,y) = (0, 2)[/tex], [tex]B'(x,y) = (-1, -2)[/tex], [tex]C'(x,y) = \left(-3,-2\right)[/tex] and [tex]D'(x,y) = (-4, -1)[/tex], respectively.
b) The points of the new quadrillateral are [tex]A'(x,y) = (-5, 5)[/tex], [tex]B'(x,y) = (-8,-7)[/tex], [tex]C'(x,y) = (-13, -7)[/tex] and [tex]D'(x,y) = (-17, -4)[/tex], respectively.
a) A dillation centered at the origin is defined by following operation:
[tex]P'(x,y) = k\cdot P(x,y)[/tex] (1)
Where:
If we know that [tex]k = \frac{1}{3}[/tex], [tex]A(x,y) = (0,6)[/tex], [tex]B(x,y) = (-3,-6)[/tex], [tex]C(x,y) = (-9, -6)[/tex] and [tex]D(x,y) = (-12, -3)[/tex], then the new points of the quadrilateral are:
[tex]A'(x,y) = \frac{1}{3}\cdot (0,6)[/tex]
[tex]A'(x,y) = (0, 2)[/tex]
[tex]B'(x,y) = \frac{1}{3} \cdot (-3,-6)[/tex]
[tex]B'(x,y) = (-1, -2)[/tex]
[tex]C'(x,y) = \frac{1}{3}\cdot (-9,-6)[/tex]
[tex]C'(x,y) = \left(-3,-2\right)[/tex]
[tex]D'(x,y) = \frac{1}{3}\cdot (-12,-3)[/tex]
[tex]D'(x,y) = (-4, -1)[/tex]
The points of the new quadrillateral are [tex]A'(x,y) = (0, 2)[/tex], [tex]B'(x,y) = (-1, -2)[/tex], [tex]C'(x,y) = \left(-3,-2\right)[/tex] and [tex]D'(x,y) = (-4, -1)[/tex], respectively. [tex]\blacksquare[/tex]
b) A translation along a vector is defined by following operation:
[tex]P'(x,y) = P(x,y) +T(x,y)[/tex] (2)
Where [tex]T(x,y)[/tex] is the transformation vector.
If we know that [tex]T(x,y) = (-5,-1)[/tex], [tex]A(x,y) = (0,6)[/tex], [tex]B(x,y) = (-3,-6)[/tex], [tex]C(x,y) = (-9, -6)[/tex] and [tex]D(x,y) = (-12, -3)[/tex],
[tex]A'(x,y) = (0,6) + (-5, -1)[/tex]
[tex]A'(x,y) = (-5, 5)[/tex]
[tex]B'(x,y) = (-3, -6) + (-5, -1)[/tex]
[tex]B'(x,y) = (-8,-7)[/tex]
[tex]C'(x,y) = (-9, -6) + (-5, -1)[/tex]
[tex]C'(x,y) = (-13, -7)[/tex]
[tex]D'(x,y) = (-12,-3)+(-5,-1)[/tex]
[tex]D'(x,y) = (-17, -4)[/tex]
The points of the new quadrillateral are [tex]A'(x,y) = (-5, 5)[/tex], [tex]B'(x,y) = (-8,-7)[/tex], [tex]C'(x,y) = (-13, -7)[/tex] and [tex]D'(x,y) = (-17, -4)[/tex], respectively. [tex]\blacksquare[/tex]
To learn more on transformation rules, we kindly invite to check this verified question: https://brainly.com/question/4801277