a) The points of the other side of the parallelogram are [tex](1, 3)[/tex] and [tex](-4,1)[/tex].
b) The points of the other side of the square are [tex](-1,0)[/tex] and [tex](4,2)[/tex].
How to find missing points of quadrilaterals
In this question we shall use vector operations and Pythagorean theorem to determine the location of the missing two points of each quadrilateral.
a) Let be [tex]A(x,y) = (-3, 5)[/tex] and [tex]B(x,y) = (2,7)[/tex] the endpoints of the line segment and [tex]C(x,y) = (-1, 4)[/tex] the point of intersection of the diagonals. The  remaining points of the parallelogram can be found by the following two formulas:
[tex]D(x,y) = A(x,y) + 2\cdot [C(x,y)-A(x,y)][/tex] (1)
[tex]E(x,y) = B(x,y) + 2\cdot [C(x,y)-B(x,y)][/tex] (2)
([tex]A(x,y) = (-3, 5)[/tex], [tex]B(x,y) = (2,7)[/tex], [tex]C(x,y) = (-1, 4)[/tex])
[tex]D(x,y) = (-3,5)+2\cdot (2,-1)[/tex]
[tex]D(x,y) = (1,3)[/tex]
[tex]E(x,y) = (2, 7) + 2\cdot (-3,-3)[/tex]
[tex]E(x,y) = (-4,1)[/tex]
The points of the other side of the parallelogram are [tex](1, 3)[/tex] and [tex](-4,1)[/tex]. [tex]\blacksquare[/tex]
b) Let be [tex]A(x,y) = (-3, 5)[/tex] and [tex]B(x,y) = (2,7)[/tex] the endpoints of the line segment, the coordinates of the missing points are found by the following two formulas:
[tex]D(x,y) = A(x,y) + (AB_{x}\cdot \cos \theta - AB_{y}\cdot \sin \theta, AB_{x}\cdot \sin \theta + AB_{y}\cdot \cos \theta)[/tex] (3)
[tex]E(x,y) = B(x,y) + \overrightarrow{AD}[/tex] (4)
Where [tex]\theta[/tex] is the rotation angle, in degrees.
([tex]A(x,y) = (-3, 5)[/tex], [tex]B(x,y) = (2,7)[/tex], [tex]\theta = -90^{\circ}[/tex])
[tex]\overrightarrow{AB} = (2+3, 7-5)[/tex]
[tex]\overrightarrow{AB} = (5,2)[/tex]
[tex]D(x,y) = (-3, 5) + (5\cdot \cos (-90^{\circ})-2\cdot \sin (-90^{\circ}), 5\cdot \sin (-90^{\circ})+2\cdot \cos (-90^{\circ}))[/tex]
[tex]D(x,y) = (-1, 0)[/tex]
[tex]\overrightarrow{AD} = (-1 + 3, 0-5)[/tex]
[tex]\overrightarrow{AD} = (2, -5)[/tex]
[tex]E(x,y) = (2,7) +(2, -5)[/tex]
[tex]E(x,y) = (4, 2)[/tex]
The points of the other side of the square are [tex](-1,0)[/tex] and [tex](4,2)[/tex]. [tex]\blacksquare[/tex]
To learn more on quadrilaterals, we kindly invite to check this verified question: https://brainly.com/question/25240753
