Polygon abcd is translated to create polygon a’b’c’d’. point a is located at (1,5) and point a’ is located at (-2,3). which expression defines the transformation of any point (x, y) to (x’,y’) on the polygons?

The translation is 3 units left and 2 units down

Step-by-step explanation:

we know that

Point A is located at (1,5) and point A’ is located at (-2,3)

so

The rule of the translation is

(x,y) > (x+a,y+b)

(1,5) > (-2,3)

Find the values  of a and b

1+a=-2 > a=-2-1 > a=-3

5+b=3 > b=3-5 > b=-2

so

The rule of the translation is

(x,y) > (x-3,y-2)

That means > The translation is 3 units left and 2 units down

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4