Math, asked by divagardivakutty, 6 months ago

show that the piont taken in onder form an isosceles triangle A(2,5) ,B(2,0),C(-2,3) RCN​

Answers

Answered by shinchen08
0

Answer:

Let ΔABC be the isosceles triangle, the third vertex be C(a,b).

and A(2,0) and B(2,5)

Let AC and BC be equal sides of the triangle

By distance formula we have,

D=

(x

2

−x

1

)+(y

2

−y

1

)

∴AB=

(2−2)

2

+(5−0)

2

=

25

=5

Now,

AC=3 [length of equal sides=3 ]

AC

2

=3

2

=9..........(a)

but by distance formula,

AC

2

=

(a−2)

2

+b

2

...........(b)

Combining (a) and (b)

⇒(a−2)

2

+b

2

=9

⇒a

2

+4−4a+b

2

=9

⇒a

2

+b

2

−4a=5 ---------- (1)

Consider BC

BC

2

=

(a−2)

2

+(b−5)

2

but BC=3

∴(a−2)

2

+(b−5)

2

=9

⇒a

2

+4−4a+b

2

+25−10b=9

⇒a

2

+b

2

−4a−10b+20=0 ------- (2)

⇒−10b+20+5=0 ---------(from 1 )

⇒10b=25

⇒b=

10

25

=

2

5

Now, a

2

+

4

25

−4a=5

⇒a

2

−4a=

4

−5

⇒a

2

−4a+

4

5

=0

⇒a=

2

16−4∗1∗

4

5

=

2

11

=

2

2+

11

,

2

2−

11

∴ Coordinate of third vertex (a,b) = (

2

2+

11

,

2

5

) and (

2

2−

11

,

2

5

)

Similar questions