If two vertices of an isosceles triangle are (2, 0) and (2, 5) and length of the equal sides is 3 then the third vertex is

(2, 6) & (-5, 3)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(8, 3) & (5, 1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(2 \pm \frac{\sqrt{11}}{2}, \frac{5}{2})

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(3 \pm \frac{\sqrt{14}}{2}, \frac{7}{2})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $(2 \pm \frac{\sqrt{11}}{2}, \frac{5}{2})$
$G i v e n - A (2, 0), B (2, 5) & C (x, y) a r e t h e v e r t i c e s o f a n i s o s c e l e s Δ A B C . T o f i n d o u t - C (x, y) = ? S o l u t i o n - U s i n g d i s t a n c e f o r m u l a, A B = \sqrt{{(2 - 2)}^{2} + {(0 - 5)}^{2}} u n i t s = 5 u n i t s \neq 3 u n i t s . ∴ A B i s t h e b a s e o f t h e g i v e n t r i a n g l e . ∴ A C = B C = 3 u n i t s . . . . . . . . . (i) ⟹ \sqrt{{(x - 2)}^{2} + {(y - 0)}^{2}} = \sqrt{{(x - 2)}^{2} + {(y - 5)}^{2}} ⟹ - 10 y + 25 = 0 ⟹ y = \frac{5}{2} . p u t t i n g y = \frac{5}{2} i n A g a i n A C = B C = 3 u n i t s ∴ \sqrt{{(x - 2)}^{2} + {(y - 0)}^{2}} = 3 (b y i) ⟹ x^{2} + y^{2} - 4 x + 4 = 9 ⟹ . x^{2} + y^{2} - 4 x - 5 = 0 P u t t i n g y = \frac{5}{2}, x^{2} + {(\frac{5}{2})}^{2} - 4 x - 5 = 0 ⟹ 4 x^{2} - 16 x + 5 = 0 ⟹ x = \frac{16 \pm \sqrt{16^{2}} - 4 \times 4 \times 5}{2} ⟹ x = 2 \pm \frac{\sqrt{11}}{2} . ∴ C (x, y) = (2 \pm \frac{\sqrt{11}}{2}, \frac{5}{2}) . N o t e - t h e \pm s i g n o f x a n d + s i g n o f y s h o w s t h a t t h e t r i a n g l e i s i n t h e f i r s t a s w e l l a s i n t h e s e c o n d q u a d r a n t . A n s - O p t i o n C .$

Suggest Corrections

Similar questions

(2, 0)

(2, 5)

3

(3, 4)

(- 2, 3)

(\frac{1 + \sqrt{3}}{2}, \frac{7 - 5 \sqrt{3}}{2})

(\frac{1 - \sqrt{3}}{2}, \frac{7 + 5 \sqrt{3}}{2})

Two vertices of an isosceles triangle (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.

(2, 1, 5)

(3, 2, 3)

Join BYJU'S Learning Program