Find the preimage of the point (4, 3) under the given transformation. a transformation t : (x, y) (x - 2, y + 3) (2, 6) (2, 3) (6, 3) (6, 0)

The preimage is

Step-by-step explanation:

The given point is (4,3).

The translation rule is

Let be the preimage.

Then,

We apply this rule to the preimage to obtain;

This implies that;

Also,

Hence the preimage is

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

ab: 2 n83b8eb7ebi. 8e yen in