Hi, I came across the following problem in the Ask and Answer section: If (a,b) is the mid-point of line - Maths - Coordinate Geometry

Question

Hi,
I came across the following problem in the Ask and Answer
section:
If (a,b) is the mid-point of line segment joining the points
A(10,-6) and B(k,4) and a-2ab=18, find the value of k and distance
AB
The expert has given the following steps:
(a,b) = (10+k/2, -6+4/2)
Comparing both sides, we get
a= 10+k/2
b= -1
Weve a relation:
a-2ab = 18
10+k/2 2 (10+k/2) (-1) = 18
I don't know how to proceed beyond this step The answer given is
k = 2 How to solve further? Kindly help

Ayush Jha · Accepted Answer

We will use section formula as-

$(a, b) = (\frac{10 + k}{2}, \frac{- 6 + 4}{2}) O n c o m p a r i n g a = \frac{10 + k}{2} b = - 1$

Now according to the given relation-

$a - 2 a b = 18 P u t t h e v a l u e s o f a a n d b (\frac{10 + k}{2}) - 2 (\frac{10 + k}{2}) (- 1) = 18 (\frac{10 + k}{2}) + 2 (\frac{10 + k}{2}) = 18 3 (\frac{10 + k}{2}) = 18 (\frac{10 + k}{2}) = 6 10 + k = 12 k = 2$