Question

The mid-point of the line segment joining \(\mathrm{A}(p, 5)\) and \(\mathrm{B}(3, q)\) is \(\mathrm{M}(-1, 4)\). Find the values of p and q.

Answer 1

Since M is the mid-point of AB,

$$\frac{p + 3}{2} = -1$$ 

$$\Rightarrow p + 3 = -2$$

$$\Rightarrow p = -5$$

$$\frac{5 + q}{2} = 4$$

$$\Rightarrow 5 + q = 8$$

$$\Rightarrow q = 3$$

Hence $$p = -5$$ and $$q = 3$$.