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प्रश्न
Point (0, –7) lies ______.
विकल्प
on the x-axis
in the second quadrant
on the y-axis
in the fourth quadrant
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उत्तर
Point (0, –7) lies on the y-axis.
Explanation:
In point (0, –7), x-coordinate is zero, so it lies on y-axis and y-coordinate is negative, therefore the point (0, –7) lies on the y-axis in the negative direction.
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The line joining the points (2, 1) and (5, −8) is trisected at the points P and Q. If point P lies on the line 2x − y + k = 0. Find the value of k.
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If (x, y) be on the line joining the two points (1, −3) and (−4, 2) , prove that x + y + 2= 0.
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If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C \[\left( \frac{3}{2}, \frac{5}{2} \right)\] , find x, y.
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Find the coordinates of the point which is equidistant from the three vertices A (\[2x, 0) O (0, 0) \text{ and } B(0, 2y) of ∆\] AOB .
If the points P(1, 2), Q(0, 0) and R(x, y) are collinear, then find the relation between x and y.
Given points are P(1, 2), Q(0, 0) and R(x, y).
The given points are collinear, so the area of the triangle formed by them is `square`.
∴ `1/2 |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = square`
`1/2 |1(square) + 0(square) + x(square)| = square`
`square + square + square` = 0
`square + square` = 0
`square = square`
Hence, the relation between x and y is `square`.
