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,
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](/tex.php?f=d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2})
![ok'=\sqrt{(2-0)^2+(4-0)^2}= \sqrt{4+16}= \sqrt{20}=2\sqrt{5}](/tex.php?f=ok'=\sqrt{(2-0)^2+(4-0)^2}= \sqrt{4+16}= \sqrt{20}=2\sqrt{5})
![ok=\sqrt{(4-0)^2+(8-0)^2}= \sqrt{16+64}= \sqrt{80}=4\sqrt{5}](/tex.php?f=ok=\sqrt{(4-0)^2+(8-0)^2}= \sqrt{16+64}= \sqrt{80}=4\sqrt{5})
put these values in equation (1).
![k=\frac{2\sqrt{5}}{4\sqrt{5}}= \frac{1}{2}](/tex.php?f=k=\frac{2\sqrt{5}}{4\sqrt{5}}= \frac{1}{2})
therefore scale factor is
and option d is correct.