If $A (2a+3b, a +6b)$ and $B (3a + 4b, 2a + 5b)$ are two points, then distance between the points A and B is:

 \(\sqrt { 2(a² + b²) }\)

Distance between two points A(x1 , y1) and B(x2 , Y2 )

= \(\sqrt { (x2 - x1 )² + (y2 - y1)² }\)

Now,

Distance between two points A (2a + 3b , a + 6b ) and B ( 3a + 4b , 2a + 5b )

= \(\sqrt { ( (3a+4b) - (2a+3b) )² + ( (2a+5b) - (a+6b) )² }\)

= \(\sqrt { ( a + b) )² + ( a - b )² }\)

= \(\sqrt { 2(a² + b²) }\)

B(3a+4b,2a+5b)