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

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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)   (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)



A(0,0),C (4,0)



B(0,6) , and C (4,0).





Triangle is similar to triangle , and the length of is units. what is the measure of segment ? why
=>similar triangles have sides





Answer by MathTherapy(10552)   (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 of side AB. So is side DF which corresponds to AC and is also of AC, or
Within what I just stated, you should be able to answer the question, "why?"
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