If ABCD forms a parallelogram- where A -0-1- B -6-7- C - 3 and D -2-3- then the value of - is

Given : A=(0, 1), B = (6, 7), C = (λ,3) and D = ( 2, 3) form a parallelogram, so nbsp; AB= CD, BC =AD ⇒ 10 = √((λ+2)^2) ⇒λ = 12, 8 √((λ 6)^2+16) = √(4+16) ⇒ ...

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Distance Formula

If ABCD forms...

Question

If $A B C D$ forms a parallelogram, where $A = (0, - 1), B = (6, 7), C = (λ, 3)$ and $D = (- 2, 3)$ , then the value of $λ$ is

Open in App

Solution

Given : $A = (0, - 1), B = (6, 7), C = (λ, 3)$ and $D = (- 2, 3)$ form a parallelogram, so
$A B = C D, B C = A D \Rightarrow 10 = \sqrt{(λ + 2)^{2}} \Rightarrow λ = - 12, 8 \sqrt{(λ - 6)^{2} + 16} = \sqrt{4 + 16} \Rightarrow λ = 4, 8 ∴ λ = 8$

Suggest Corrections

Similar questions

Q. If

A B C D

forms a parallelogram, where

A = (0, - 1), B = (6, 7), C = (λ, 3)

and

D = (- 2, 3)

, then the value of

λ

Q. Question 11
The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3), B(6,7) and C(8,3) is
(A) (0, 1)
(B) (0, –1)
(C) (–1, 0)
(D) (1, 0)

Q. Question 11
The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3), B(6,7) and C(8,3) is
(A) (0, 1)
(B) (0, –1)
(C) (–1, 0)
(D) (1, 0)

If the equations $x^{2} + 2 λ x + λ^{2} + 1 = 0, λ ϵ R a n d a x^{2} + b x + c = 0$ where a, b, c are lengths of sides of triangle have a common root, then the possible range of values of $λ$ is