Question

the three vertices of a triangle are (3,0),(6,0),(x,y).find x and y

Answer 1

Let A (3,0) B (6,0) C(x,y)
ABC will be triangle when
AB=BC=CA
using distance formula
AB=√{(6-3)^2 + 0}= 3
BC= √{(x-6)^2 +y^2}
CA=√{(x-3)^2 +y^2}
Now, AB=BC
then 3= √{(x-6)^2 +y^2}
9= (x-6)^2 +y^2 ---i
BC=CA
Then, √{(x-6)^2 +y^2 =√{(x-3)^2 + y^2}
(x-6)^2 +y^2 =(x-3)^2 +y^2
x^2 -12x +36= x^2 -3x+9
-12x+36= -6x+9
-6x= -27
x=9/2
now, putting x in equation (i)
9= (9/2-6)^2 +y^2
9= 9/4 +y^2
27/4=y^2
y=+,- 3√3/4
Hence, C(x,y) = (9/2,3√3/2) and (9/2,-3√3/2).

HOPE IT HELPS YOU.

Answer 2

Question isnt complete