The vertices of triangle abc are a(2,3), b(–1,2), and c(3,1). if δdef ∼ δabc and de = 4ab, what is the length of ef? √10 √17 4√10 4√17

Option D is correct

4√17

Step-by-step explanation:

Similar triangle states that the corresponding sides are in proportion.

As per the statement:

The vertices of triangle ABC are A(2,3), B(–1,2), and C(3,1).

If ΔDEF ∼ ΔABC and DE = 4AB

⇒

by definition of similar triangle In ΔDEF ∼ ΔABC,

⇒         ...[1]

We have to find EF:

form [1] we have;

Using distance(D) formula:

Apply the distance formula to find BC:

⇒

⇒

then;

Therefore,  the length of EF is, 4√17

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.