SOLUTION: traingle ABC has coordinates A(0,0), B(0,6) , and C (4,0). Triangle DEF is similar to triangle ABC, and the length of DE is 3 units. what is the measure of segment DF? why

Algebra ->  Triangles -> SOLUTION: traingle ABC has coordinates A(0,0), B(0,6) , and C (4,0). Triangle DEF is similar to triangle ABC, and the length of DE is 3 units. what is the measure of segment DF? why      Log On


   

Question 1135262: traingle ABC has coordinates A(0,0), B(0,6) , and C (4,0). Triangle DEF is similar to triangle ABC, and the length of DE is 3 units. what is the measure of segment DF? why
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

triangle ABC has coordinates A(0,0), B(0,6) , and C (4,0).
distance between two points is equal to length of the side
A(0,0), B(0,6)
AB=sqrt%28%280-0%29%5E2%2B%286-0%29%5E2%29
AB=sqrt%2836%29
AB=6
A(0,0),C (4,0)
AC=sqrt%28%284-0%29%5E2%2B%280-0%29%5E2%29
AC=sqrt%2816%29
AC=4
B(0,6) , and C (4,0).
BC=sqrt%28%284-0%29%5E2%2B%280-6%29%5E2%29
BC=sqrt%2816%2B36%29
BC=sqrt%2852%29
BC=4sqrt%2813%29

Triangle DEF is similar to triangle ABC, and the length of DE is 3 units. what is the measure of segment DF? why
AC%2FDF=AB+%2FDE+=>similar triangles have proportional sides
4%2FDF=6+%2F3
12=6+DF
DF=12%2F6
DF=2

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

traingle ABC has coordinates A(0,0), B(0,6) , and C (4,0). Triangle DEF is similar to triangle ABC, and the length of DE is 3 units. what is the measure of segment DF? why
Side AB is on the y-axis, and having the same x-coordinate, has a length that is the ABSOLUTE difference between the y-coordinates. Therefore, AB = |0 - 6| or |6 - 0| = 6 units

Side AC is on the x-axis, and having the same y-coordinate, has a length that is the ABSOLUTE difference between the x-coordinates. Therefore, AC = |0 - 4| or |4 - 0| = 4 units

DE = 3 units in the smaller right-triangle CORRESPONDS to AB in the larger right-triangle, and so, it's obvious that DE is 1%2F2 of side AB. So is side DF which corresponds to AC and is also 1%2F2 of AC, or highlight_green%28matrix%281%2C6%2C+1%2F2%2C+of%2C+4%2C+%22=%22%2C+2%2C+units%29%29

Within what I just stated, you should be able to answer the question, "why?"