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
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)
The correct answer is:
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.
To determine if two polygons are similar, we need to check if their corresponding sides are proportional and their corresponding angles are congruent.
In this case, we can see that the corresponding sides of ABCD and A'B'C'D' are proportional since they have the same length and orientation.
However, when we try to map A'B'C'D' to EFGH using a dilation, the corresponding sides are not proportional. A dilation is a transformation that multiplies the coordinates of a point by a scale factor. In this case, the scale factor would be (2, 3) since we need to multiply the x-coordinates by 2 and the y-coordinates by 3.
To see this, let's compare the side lengths of A'B' and EF. The length of A'B' is |(-2+4)-(-5+4)| = 3, and the length of EF is |(4-(-2))-(4-(-2))| = 12. These lengths are not proportional since 3 is not equal to 12 multiplied by any constant factor.
Therefore, we can conclude that the polygons ABCD and EFGH are not similar.
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 !