The figure shows a rhombus ABCD where the diagonals AC and BD intersect at E. Find the value of x.

2

Step-by-step explanation:

Using the Z rule, we get the angle of DCE is 2x + 53

The angle DEC is a right angle as the diagonals of a rhombus always make a right angle

So we get the equation

3x + 7 + 2x + 53 + 90 = 180

5x = 10

x = 2

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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