Triangle j'k'l' shown on the grid below is a dilation of triangle jkl using the origin as the center of dilation: which scale factor was used to create triangle j'k'l'? a. 4 b. 1 / 4 c. 2 d. 1 / 2

answer: the correct option is d.

explanation:

it is given that the triangle j'k'l' shown on the grid below is a dilation of triangle jkl using the origin as the center of dilation.

from the given graph it is noticed that k(4,8) and k'(2,4). let origin is defined by o and scale factor is defined by k, then

    (1)

distance formula,

put these values in equation (1).

therefore scale factor is     and option d is correct.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8