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प्रश्न
Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
उत्तर
Let P (x ,0) be the point on . x- axis Then
AP = BP ⇒ AP2 = BP2
`⇒ (x+1)^2 + (0-0)^2 = (x-5)^2 +(0-0)^2`
`⇒ x^2 +2x+1=x^2-10x +25`
`⇒ 12x = 24 ⇒ x = 2`
Hence , x = 2
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संबंधित प्रश्न
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when The centre of the square is at the origin and coordinate axes are parallel to the sides AB and AD respectively.
Find a point on the x-axis which is equidistant from the points (7, 6) and (−3, 4).
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(4, 5) B(7, 6), C (4, 3), D(1, 2)
Find the ratio in which the point (2, y) divides the line segment joining the points A (-2,2) and B (3, 7). Also, find the value of y.
Prove that the points (4, 5) (7, 6), (6, 3) (3, 2) are the vertices of a parallelogram. Is it a rectangle.
Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).
Find the coordinates of the midpoints of the line segment joining
A(3,0) and B(-5, 4)
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
If the points P, Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B(7, 10) in 5 equal parts, find x, y and p.
If P (x, 6) is the mid-point of the line segment joining A (6, 5) and B (4, y), find y.
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
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The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is
The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) are
The points whose abscissa and ordinate have different signs will lie in ______.
If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).
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`
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Statement A (Assertion): If the coordinates of the mid-points of the sides AB and AC of ∆ABC are D(3, 5) and E(–3, –3) respectively, then BC = 20 units.
Statement R (Reason): The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.
Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1
Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.
