Question

The pointe A. (1,-2), B(2, 3) c(K/2)
and D(-1, -3) are the vertices of a
parallelogram Find the value of k​

Answer 1

❏ Used Formula

If a straight line AB is intersected by a line at point p in the ratio m:n ,where the coordinates of P(x,y),A(x1,y1) and B(x2,y2), then;

$\sf\longrightarrow x=\frac{mx_2+nx_1}{m+n}$

$\sf\longrightarrow y=\frac{my_2+ny_1}{m+n}$

now, if m=n (i.e., midpoint) then.

$\sf\longrightarrow x=\frac{x_2+x_1}{2}$

$\sf\longrightarrow y=\frac{y_2+y_1}{2}$

❏ Solution

❰ Now we know that for a parallelogram the diagonals bisected each other .

i.e., midpoint of the both diagonals is same ❱

Here, The parallelogram is ABCD ,

And it's diagonals are AC and BD,

Let the midpoint is O

i.e., They bisect each other at point O.

Now , The midpoint of the diagonal BD.

$\sf\longrightarrow (\frac{2-1}{2}\:,\:\frac{-3+3}{2})$

$\sf\longrightarrow (\frac{1}{2}\:,\:0)$

Now , The midpoint of the diagonal AC

$\sf\longrightarrow (\frac{1+k}{2}\:,\:\frac{-2+2}{2})$

$\sf\longrightarrow (\frac{1+k}{2}\:,\:0)$

Now, comparing , ordinates.

$\sf\longrightarrow \frac{1+k}{2}=\frac{1}{2}$

$\sf\longrightarrow 1+k=1$

$\sf\longrightarrow\boxed{ k=0}$

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

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