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प्रश्न
If (1, −2), (3, 6), (x, 10) and (3, 2) are the vertices of the parallelogram taken in order, then the value of x is
विकल्प
6
5
4
3
उत्तर
5
Explanation;
Hint:
Since ABCD is a parallelogram
Mid-point of AC = Mid-point of BD
`((1 + x)/2, (-2 + 10)/2) = ((3 + 3)/2, (6 + 2)/2)`
`(1 + x)/2 = 6/2`
⇒ 1 + x = 6
⇒ x = 6 – 1 = 5
The value of x = 5
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Solution :
Suppose, (–4, 2) = (x1, y1) and (6, 2) = (x2, y2) and co-ordinates of P are (x, y).
∴ According to the midpoint theorem,
x = `(x_1 + x_2)/2 = (square + 6)/2 = square/2 = square`
y = `(y_1 + y_2)/2 = (2 + square)/2 = 4/2 = square`
∴ Co-ordinates of midpoint P are `square`.
