Question

If (a,b) is the mid-point of the line segment joining the point s A(10,-6),B(k,4) and a-2b=18. Find the value of k and the distance AB.

Answer 1

Value of k is 22

Distance of AB is
$2 \sqrt{61} units$


Please refer the above photograph for the used process.



KEY POINTS TO REMEMBER :-

1) DISTANCE FORMULA :-

$= \sqrt{ {((x \frac{}{2} )- (x \frac{}{1} )) }^{2} + ((y\frac{}{2}) - (y \frac{}{1}) )^{2}}$

2)SECTION FORMULA :-

$x = \frac{mx2 + nx1}{m + n} \\ \\ y = \frac{my2 + ny1}{m + n}$


3) MID POINT SECTION FORMULA :-

$x = \frac{x2 + x1}{2} \\ \\ y = \frac{y2 + y1}{2}$


Thanks!