Question

Find the co-ordinates of a point whose abscissa is 10 and its distance from the point (2, –3) is 10 units.

Answer 1

Given: Abscissa = 10 ⇒ point P = (10, y). Its distance from (2, –3) is 10 units.

Distance formula: `sqrt((10 - 2)^2 + (y - (-3))^2) = 10`

⇒ `sqrt(8^2 + (y + 3)^2) = 10`

⇒ `64 + (y + 3)^2 = 100`

⇒ `(y + 3)^2 = 36`

⇒ y + 3 = ±6

So, y = 3 or y = –9.

The required points are (10, 3) and (10, –9).