Question

If P(-1,1) is the midpoint of the line segment joining A(-3,b) and B(1, b+4) then b = ? 

(a) 1 

(b) -1 

(c) 2 

(d) 0

Answer 1

Correct answer is (b) -1

The given ports are A(-3,b) and B(1,b + 4).

Then, (x₁ = -3,y₁ = b) and (x₂ = 1,y₂ = b + 4)

Therefore,

\(x=\frac{[(-3)+1]}{2}\)

= \(\frac{-2}{2}\)

= -1

And

\(y=\frac{[b\,+\,(b\,+\,4)]}{2}\)

= \(\frac{2b\,+\,4}{2}\)

= b + 2

But the midpoint is P(-1,1).

Therefore,

b + 2 = 1

\(\Rightarrow b=-1\)