Answer:
the answer is the option A
They are similar because Line BR : Line DB is \(1:2\) and line KE : Line YK \(1:2\)
Step-by-step explanation:
we know that
If the figures are similar
then
the ratio of their corresponding figures are equal
so
\(\frac{BR}{KE}=\frac{DB}{YK}\)
Find the distances
the formula to calculate the distance between two points is equal to
\(d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}\)
Find the distance BR
substitute the values
\(d=\sqrt{(4-6)^{2}+(6-5)^{2}}\)
\(d=\sqrt{(-2)^{2}+(1)^{2}}\)
\(dBR=\sqrt{5}\ units\)
Find the distance KE
substitute the values
\(d=\sqrt{(11-9)^{2}+(10-6)^{2}}\)
\(d=\sqrt{(2)^{2}+(4)^{2}}\)
\(dKE=2\sqrt{5}\ units\)
Find the distance DB
substitute the values
\(d=\sqrt{(6-4)^{2}+(5-1)^{2}}\)
\(d=\sqrt{(2)^{2}+(4)^{2}}\)
\(dDB=2\sqrt{5}\ units\)
Find the distance YK
substitute the values
\(d=\sqrt{(9-1)^{2}+(6-10)^{2}}\)
\(d=\sqrt{(8)^{2}+(-4)^{2}}\)
\(dYK=4\sqrt{5}\ units\)
substitute
\(\frac{BR}{KE}=\frac{DB}{YK}\)
\(\frac{\sqrt{5}}{2\sqrt{5}}=\frac{2\sqrt{5}}{4\sqrt{5}}\)
\(\frac{1}{2}=\frac{2}{4}\)
\(\frac{1}{2}=\frac{1}{2}\) --------> the figures are similar
\(\frac{BR}{KE}=\frac{DB}{YK}\)-----> rewrite
\(\frac{BR}{DB}=\frac{KE}{YK}\)
substitute the values
\(\frac{\sqrt{5}}{2\sqrt{5}}=\frac{2\sqrt{5}}{4\sqrt{5}}\)
simplify
\(\frac{1}{2}=\frac{2}{4}\) ------> \(\frac{1}{2}=\frac{1}{2}\)
