# 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 ,

Therefore, the coordinates of the third vertex are: ;

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