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.
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: ;