Question

\(\mathrm{A}(-3, b)\) and \(\mathrm{B}(1, b + 4)\) are two points. If the coordinates of the mid-point of AB are \((-1, 1)\), then the value of b is ______.

Options

• –1

• 0

• 1

• 2

Answer 1

\(\mathrm{A}(-3, b)\) and \(\mathrm{B}(1, b + 4)\) are two points. If the coordinates of the mid-point of AB are \((-1, 1)\), then the value of b is –1.

Explanation:

The y-coordinate of the mid-point gives \(\frac{b + (b + 4)}{2} = 1 \Rightarrow 2b + 4 = 2 \Rightarrow b = -1\). The x-coordinate \(\frac{-3 + 1}{2} = -1\).