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.

Question

Philoid · Accepted Answer

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

,

Also, PA = 3

On squaring both sides, we get

On substituting ,

Using quadratic formula:

Therefore coordinates of third vertex are: ;