Question

If the mid-point (x, y) of the line joining (3, 4) and (p, 7) lies on 2x + 2y + 1 = 0, then what will be the value of p?

Answer 1

Mid−point of a line = `((x_1 + x_2)/2, (y_1 + y_2)/2)`

(x, y) = `((3 + "p")/2, (4 + 7)/2)`

= `((3 + "p")/2, 11/2)`

The point `((3 + "p")/2, 11/2)` lies on 2x + 2y + 1 = 0

`2((3 + "p")/2) + 2 11/2 + 1` = 0

3 + p + 11 + 1 = 0

⇒ p + 15 = 0

⇒ p = −15

The value of p is −15.