If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0, find the value of k.

Question

Philoid · Accepted Answer

Let A(3, 4) and B(k, 7) and midpoint be C(x, y) which lies on the line 2x+2y+1 = 0

By midpoint formula,

x = , y =

For point C(x, y),

x = , y = …(1)

Here, y = ,

Hence, substituting value of y in given equation of line,

2x + 2 × + 1 = 0

∴ 2x = -12

∴ x = -6

Now substituting value of x in equation(1), we get.

x =

-6 =

∴ -12 = 3 + k

∴ k = -15

Hence, the value of k is -15.