Question

Determine whether the polygons with the given vertices are similar.

Quadrilateral ABCD with vertices: A(-5, 4), B(-2, 4), C(-2, 2), D(-5, 2)
Quadrilateral EFGH with vertices: E(-2, 0), F(4, 0), G(4, -6), H(-2, -6)
a
The polygons are similar. ABCD can be mapped to A'B'C'D' by a translation (x, y)-->(x-4, y+4) A'B'C'D' can be mapped to EFGH by a dilation (x, y)-->(2x, 3y)
b
The polygons are not similar. ABCD can be mapped to A'B'C'D' by a translation (x, y)-->(x+4, y-4) But A'B'C'D' cannot be mapped to EFGH by a dilation
c
The polygons are similar. ABCD can be mapped to A'B'C'D' by a translation (x, y)-->(x+4, y-4) A'B'C'D' can be mapped to EFGH by a dilation (x, y)-->(2x, 3y)
d
The polygons are not similar. ABCD can be mapped to A'B'C'D' by a translation (x, y)-->(x-4, y+4) But A'B'C'D' cannot be mapped to EFGH by a dilation

Answer 1

evidently we can translate or dilate but not rotate

look at slopes(up and down is oo)
first one ab=0 bc=oo cd=0 da=oo
so a rectangle with long side = 3 and short = 2

now the second one slopes
all zero or vertical again
long side = 6 , short side = 6
This one is a SQUARE
a rectangle with length to width of 3/2 is not similar to a square.

Draw it !