Question

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

Answer 1

(a,b)=((10+k)/2,5)

a=5+k/2

b=5

a-10=18

a=28

28=5+k/2

k/2=23

k=46

AB=√(10-46)^2+(6-4)^2

AB=√216+4

AB=√220

AB=2√55

Answer 2

by the way hey

here is your answer dear

Answer:

Given,

(a,b) is the midpoint of the a(10,-6) and b(k,4).

a-2b=16.

we know that,

Midpoint = (x1+x2/2), (y1+y2/2)

(a,b)=(10+k/2),(-6+4/2)

(a,b)=(10+k/2),(-2/2)

(a,b)=(10+k/2),(-1)

by comparing on both sides

a=10+k/2 , b=-1

we know that,

a-2b=16

=> 10+k/2 -2(-1)=16

=> 10+k/2+2=16

=>10+k/2=14

=>10+k=28

=>k=18