Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.

Given: Vertices (2, 0) and (2, 5).

To find: The third vertex

Formula Used:

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

Distance

Explanation:

Vertices of an isosceles are A (2, 0) and B (2, 5).

Let the third vertex is P (x, y)

Using distance formula

Length of side PA units

Length of side PB units

Since PA = PB

On squaring both sides, we get

(x - 2)² + y² = (x - 2)² + (y - 5)²

x² - 4x + 4 + y² = x² - 4x + 4 + y² - 10y + 25

,

Also, PA = 3

On squaring both sides, we get

(x - 2)² + (y)² = 9

x² - 4x + 4 + y²= 9

x² - 4x + y² = 5

On substituting ,

Using the quadratic formula:

Therefore, the coordinates of the third vertex are: ;