Question

if (x1,y1) and( x2,y2) are the vertices of base of an isosceles triangle and the angle made by the side with the base is theta then third vertex is ​

Answer 1

Step-by-step explanation:

ANSWER

Two vertices of an equilateral triangle are (0,0)and(3,√3).

Let the third vertex of the equilateral triangle be (x,y)

Distance between (0,0)and(x,y) = Distance between(0,0)and(3,√3) = Distance between (x,y)and(3,√3)

(x

2

+y

2

)

=

(3

2

+3)

=

(x−3)

2

+(y−

3

)

2

x

2

+y

2

=12

x

2

+9−6x+y

2

+3−2

3y

=12

24−6x−2

3y

=12

−6x−2

3y

=−12

3x+

3y

=6

x=

3

6−

3y

3

(6−

3y

)

2+y

2

=12

9

(36+3y2−12

3y

)

+y

2

=12

36+3y

2

−12

3y

+9y2=108

−12

3y

+12y

2

−72=0

−3y

+y2−6=0

(y−2

3

)(y+

3

)=0

y=2

3

or

−3

Ify=2

3

,x=(6−6)/3=0

Ify=−

3

,x=

3

9

=3

So,the third vertex of the equilateral triangle=(0,2

3

)or(3,−

3

).