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) ⇒ ...

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Standard XIII

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

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Solution

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

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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. If the points

A (- 2, - 1), B (1, 0), C (a, 3)

and

D (1, b)

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Q. If A (-2, 1) B (1 , 0), C (x , 3 ) and D (1, Y) are the vertices of a Parallelogram ABCD, then find the values of x and y.

Q. Question 6
If angles A, B, C and D of the quadrilateral ABCD, taken in order are in the ratio 3: 7: 6: 4, then ABCD is a
(A) rhombus
(B) parallelogram
(C) trapezium
(D) kite

Q. (a) a,b,c are lengths of sides of an scalene triangle. If equation

x^{2} + 2 (a + b + c) x + 3 λ (a b + b c + a c) = 0

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λ < \frac{4}{3}

(b)

\frac{11}{3} < λ < \frac{17}{3}

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\frac{11}{6} < λ < \frac{15}{4}

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λ \geq 1

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x^{2} - 10 c x - 11 d = 0

and c,d are the roots of

x^{2} - 10 a x - 11 b = 0

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

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

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

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