We are given that the angle a is the right angle. So let
us work from this.
ab = 12 (the vertical side of the triangle)
bc = 13 (which if drawn can be clearly observed to be the
hypotenuse) = the side opposite to angle a
ca = 5 (the horizontal side of the triangle)
 
Since we are to find for the cosine ratio of angle c or
angle θ, therefore:
cos θ = adjacent side / hypotenuse
cos θ = ca / bc
cos θ = 5 / 13
 
Check out the attached image below for the illustration
of the triangle.
 
        
             
        
        
        
Let's start with a picture.
We see RST is smaller, and BC is parallel to but in the opposite direction to its corresponding segment ST.  Both have slope -1.
If we look at the difference of points (technically called vectors but we don't have to go there) we get
C-B=(-2,2)
T-S=(1,-1)
Without further calculation we can see T-S is half the length of C-B.
The problem asks for a dilation followed by a reflection.   We know the dilation scale is k=1/2 because the new triangle is half the size.  
After dilation we get A'B'C':
A'(3,2), B'(-1,0), C'(-2,1)
We see now we need a reflection that flips the coordinates x and y.  That's the +45° line through the origin, namely y=x.
Answer: k=1/2, y=x
 
        
                    
             
        
        
        
The image of circle A is missing, so i have attached it;
Answer:
x = 17
Step-by-step explanation:
In Δs EAB and EAD
We are told that; 
∠BAE ≅ ∠DAE
AB = AD = AE
Now, 
The Two triangles have two corresponding equal sides and the angles between them are equal, thus, we can say that the two triangles are congruent by SAS (Side Angle Side) postulate of congruence
By using the result of congruence, we can say that;
EB ≅ ED
We are given that;
EB = 3x - 24 and ED = x + 10
Thus, 
3x - 24 = x + 10
∴ 3 x - 24 = x + 10
Add 24 to both sides to give;
3x = x + 34
Subtract x from both sides to give;
2x = 34
Divide both sides by 2 to give;
x = 17
 
        
                    
             
        
        
        
(12 x 15)m< 68
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I hope this helps! I couldn’t get the line below the sign lol. Sorry if wrong