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प्रश्न
If the mid-point (x, y) of the line joining (3, 4) and (p, 7) lies on 2x + 2y + 1 = 0, then what will be the value of p?
उत्तर
Mid−point of a line = `((x_1 + x_2)/2, (y_1 + y_2)/2)`
(x, y) = `((3 + "p")/2, (4 + 7)/2)`
= `((3 + "p")/2, 11/2)`
The point `((3 + "p")/2, 11/2)` lies on 2x + 2y + 1 = 0
`2((3 + "p")/2) + 2 11/2 + 1` = 0
3 + p + 11 + 1 = 0
⇒ p + 15 = 0
⇒ p = −15
The value of p is −15.
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Find the midpoint of the line segment joining the following pair of point :
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Point P is the centre of the circle and AB is a diameter. Find the coordinates of points B if coordinates of point A and P are (2, – 3) and (– 2, 0) respectively.
Given: A`square` and P`square`. Let B (x, y)
The centre of the circle is the midpoint of the diameter.
∴ Mid point formula,
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Hence coordinates of B is (– 6, 3).
