First some rewriting:
We see that the numerators of both fractions 
and a term in the denominators 
will cancel:
Then
A transformation of the plane is an isometry if, for all points X and Y, the distance between the image points X' and Y' equals the distance between X and Y. In other words, an isometry is a transformation which preserves distance
Answer:
The coordinates of k are (-2,-1)
Step-by-step explanation:
Here, we are interested in calculating the coordinates of point k.
Mathematically, we will use the internal division formula for this;
This would be;
(x,y) =( nx1 + mx2)/(m + n), (ny1 + my2)/(m + n)
where m = 1 , n = 4
x1 = -2 , x2 = 8
y1 = -4 , y2 = 11
we now make the substitutions into the formula;
(x,y) = 4(-2) + 1(-2)/(1+4) , 4(-4) + 1(11)/(4 + 1)
(x,y) = (-8-2)/5 , (-16 + 11)/5
(x,y) = -10/5 , -5/5
(x,y) = (-2, -1)
2/a= a/50
Cross multiply:
a* a= 2*50
⇒ a^2= 100
⇒ a= √100 or a= -√100
⇒ a= 10 or a= -10
Final answer: a= 10 or a= -10~
