5)The coordinates after reflection across the x-axis are: D'(2,-6), O'(5,-5), and G'(1,-1).
6) The coordinates after a 180⁰ rotation are: H'(-1,-5), E'(-3,-6), L'(-4,-3), and P'(-2,-1).
7) The coordinates after transformation are:
S' (-1,-8), T'(2,-3), A'(7,0) and R'(4,-5).
What is transformation of figure?
5) When a point is reflected across the x-axis, negate the y-coordinate while the x-axis remains unchanged.
Therefore, for the triangle with vertices D(2,6), O(5,5), and G(1,1), the coordinates after reflection across the x-axis are: D'(2,-6), O'(5,-5), and G'(1,-1).
6) When a point (x, y) is rotated by 180⁰, both x and y coordinates are negated.
So, for the quadrilateral HELP with vertices H(1,5), E(3,6), L(4,3), and P(2,1), the coordinates after a 180⁰ rotation are: H'(-1,-5), E'(-3,-6), L'(-4,-3), and P'(-2,-1).
7) For the rhombus STAR with vertices S(-3,-2), T(0,3), A(5,6), and R(2,1), applying the transformation (x,y) → (x + 2, y - 6) the new coordinates
S' (-3 + 2, -2 -6) = (-1,-8)
T'(0 + 2, 3 -6) = (2,-3)
A'(5 + 2, 6 - 6) = (7,0)
R'(2 + 2, 1 - 6) = (4,-5).
The coordinates after transformation are:
S' (-1,-8), T'(2,-3), A'(7,0) and R'(4,-5).