The smaller triangle is a pre-image of the bigger triangle. the center of dilation is (1, −1).

what is the scale factor used to create the dilation?

a 1/4
b 6
c -4
d 4

The scale factor is

Step-by-step explanation:

Lets have a look to the co-ordinates of triangle ABC and A'B'C.

The point of C= and B=

The point of C=  and A'=

By applying distance formula we can calculate the distance of line segment :

BC ===2

Similarly CA==8

Scale factor = K===4

The image and its preimage lies in opposite sides of center of dilation, C= therefore the scale factor will be negative.

Our final answer = -4

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this