Question

If A (-2, -1), B (k, 0), C (4, P) and (1, 2) are the vertices of a
parallelogram find the value of K and P.​

Answer 1

Question :-

If A(-2, -1), B(k, 0), C(4, P) and D(1, 2) are the vertices of a parallelogram find the value of K and P.

Answer :-

k = 1 and P = 3

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Step by step explaination :-

We are given the coordinates,

• A(-2, -1)
• B(k, 0)
• C(4, P)
• D(1, 2)

In a parallelogram, diagonals bisect each other.

•°• Midpoint of AC = Midpoint of BD

----> AC = BD

Using midpoint formula,

$\rightarrow (\frac{ - 2 + 4}{2}, \: \frac{ - 1 + p}{2} ) = (\frac{ k + 1}{2}, \: \frac{ 0 + 2}{2}) \\ \rightarrow \: (\frac{ 2 }{2}, \frac{- 1 + p}{2} ) = (\frac{ k + 1}{2}, \: \frac{ 2}{2} ) \\ \\ \sf \: \underline{\: (equating \: x \: coordinates)} \\ \rightarrow \: \frac{2}{2} = \frac{k + 1}{2} \\ \rightarrow \: 2 = k + 1 \\ \rightarrow \: 2 - 1 = k \\ \rightarrow \: 1 = k \\ \therefore \: k \: = 1 \\ \\ \sf \underline{\: (equating \: y \: coordinates)} \\ \rightarrow \: \frac{2}{2} = \frac{ - 1 + p}{2} \\ \: \rightarrow \: 2 = - 1 + p \\ \rightarrow \: 3 = p \\ \therefore \: p = 3$

Answer 2

Answer:

Value of P = 3

and of k = 1

Step-by-step explanation:

We are given the Vertices of the parallelogram,

•A(-2,-1)

•B(k,0)

•C(4,P)

•D(1,2)

We know that the diagonals of a parallelogram bisect each other ,

So

Mid point of AC = Mid point of BD

$\implies( \frac{4 - 2}{2} ,\frac{ P - 1}{2} ) = ( \frac{1 + k}{2} , \frac{2 + 0}{2} ) \\ \implies( \frac{2}{2} , \frac{P - 1}{2} ) = ( \frac{1 + k}{2} , \frac{2}{2} ) \\ \implies( 1, \frac{P - 1}{2} ) = ( \frac{1 + k}{2} ,1)$

Now by equating the values we have

$1 = \frac{1 + k}{2} \\ \implies2 = 1 + k \\ \implies k = 1$

And for the other one

$\frac{</u></strong><strong><u>P</u></strong><strong><u> - 1}{2} = 1 \\ \implies </u></strong><strong><u>P</u></strong><strong><u> - 1 = 2 \\ \implies </u></strong><strong><u>P</u></strong><strong><u> = 3$