Triangle DEF has vertices D (-3, -2), E (4, 4), F (4, -1). What are the coordinates of F after the triangle is rotated counterclockwise about the origin? F' (2, -3)

F' (-1, -4)

F' (1, 4)

F' (-4, 4)

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

source:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

a 360 degree rotation

step-by-step explanation:

the surface area is 124cm²

step-by-step explanation:

length: 4cm

width: 9cm

height:   2cm