if the points A(1,-2), B(2,3), C(-3,2) and D (-4,-3) are the vertices of a parallelogram ABCD then taking AB as the base, find the height of a parallelogram.
Answers
Answer:
Step-by-step explanation:
Consider a ||gram whose vertices are A(1,-2), B(2,3), C(-3,2) and D(-4,-3).
Construction :- Draw a perpendicular(DL) to the base AB from D.
DL is the height of the parallelogram if base is AB.
Let D≡(p,q).
Evaluation :-
Slope of a line = (y₂ - y₁)/(x₂ - x₁)
∴ slope of line AB = (3 + 2)/(2 - 1) = 5 = m₁ (say)
slope of line AL = slope of line AB = m₁ = (q + 2)/(p - 1)
(q + 2)/(p - 1) = 5
⇒ q + 2 = 5p - 5
⇒ 5p - q = 7 --------------------- (i)
slope of line DL = m₂ = (q + 3)/(p + 4).
We know that product of slopes of two perpendicular lines = -1
i.e, m₁ × m₂ = -1
⇒ 5 × m₂ = -1
⇒ m₂ = -1/5
∵ m₂ = (q+3)/(p+4)
⇒ (q+3)/(p+4) = -1/5
⇒ -p - 4 = 5q + 15
⇒ 5q + p = -19 -----------------------(ii)
After solving the equation i) and (ii)
p = 9/13
and q = -46/13
∴ L(9/13, -46/13) and D(-4, -3)
Now you can find length of DL .
DL = 61.4/13
Therefore height of ||gram = DL + 61.4/13 unit
Answer:
Step-by-step explanation:
Answer is 12√26/13
=12×5.09÷13
=61.18/13
=4.706 units
