Question

if the midpoint of the line segment joining the points A( 3,4) and B(K,6) is P (X, Y) and X + Y - 10=0, find the value of k

Answer 1

X coordinate of P=X
K+3/ 2=X
And,
Y coordinate of P=6+4/2=5
Now,
X+Y-10=0
K+3/ 2+5-10=0
K+3/ 2=5
K+3=10
K=7

Answer 2

Mid point of A(a,b) and B(c,d) is ((a+b)/2, (c+d)/2),

Given that Mid point of A(3,4) and B(K,6) is P(X,Y)
=> P = A+B/2
=> ((3+k)/2 , (6+4)/2)
=> ((3+k)/2, 5) = (X,Y)
=> Y = 5 and X = (3+k)/2,

Also X + Y = 10 
=> (3+k)/2 + 5 = 10,
=> k = 7,

Therfore the value of K is 7, Hope you understand, Have a great day !