The length of a line segment is of 10 units, and the coordinates of one end - point are (2, - 3). If the abscissa of the other end is 10, find the ordinate of the other end.

Given: Length = 10 units

One point = (2, - 3)

Abscissa of other points = 10

To find: The ordinate of another point.

Formula Used:

The distance between the points (x₁, y₁) and (x₂, y₂) is:

Explanation:

Let the ordinate of another end is “k”.

Applying distance formula, we get,

On squaring both sides, we get

Apply the formula:

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

⇒100 = 64 + k² + 6k + 9

⇒k² + 6k – 27 = 0

⇒k² + 9k - 3k – 27 = 0

⇒ k(k + 9) - 3(k + 9) = 0

⇒ (k - 3)(k + 9) = 0

⇒ k = 3; k = - 9;

Therefore, ordinates are 3, - 9.