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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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