How many triangles in the diagram can be mapped to one another by similarity transformations? A. 2 B. 4 C. 0 D. 3
2 answers:
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Answer:
The solution is given below:
Step-by-step explanation:
As we know the value of k and r so the equation will be
Using a graphical tool we obtain that the solution of this system
(intersection between the lines)
is given by the point (x,y) = (2,4)
(intersection between the lines)
is given by the point (x,y) = (2,4)
First notice that the triangle with sides 
and the triangle with sides 
are similar. This is true because the angle between sides 
in the smaller triangle is clearly 
, while the angle between sides 
in the larger triangle is clearly 
. So the triangles are similar with sides corresponding to 
, respectively.
Now both triangles are
, which means there's a convenient ratio between its sides. If the length of the shortest leg is 
, then the length of the longer leg is 
and the hypotenuse has length 
.
Since
is the shortest leg in the larger triangle, it follows that 
, so 
Now both triangles are
Since