Advertisements
Advertisements
प्रश्न
Find x if distance between points L(x, 7) and M(1, 15) is 10.
उत्तर १
L(x, 7), M(1, 15), and LM = 10.
By distance formula,
∴ LM = `sqrt((x − 1)^2 + (7 − 15)^2)`
∴ 10 = `sqrt((x - 1)^2 + (− 8)^2)`
Squaring both the sides, we get,
∴ 100 = (x − 1)2 + 64
∴ (x − 1)2 = 100 − 64
∴ (x − 1)2 = 36
Taking square roots of both the sides,
∴ x − 1 = `+-` 6
∴ x − 1 = 6 or x - 1 = −6
∴ x = 6 + 1 or x = −6 + 1
∴ x = 7 or x = −5
x = 7 or x = −5
उत्तर २
L(x, 7), M(1, 15), and LM = 10.
By distance formula,
∴ LM = `sqrt((x − 1)^2 + (7 − 15)^2)`
∴ 10 = `sqrt((x - 1)^2 + (− 8)^2)`
Squaring both the sides, we get,
∴ 100 = (x − 1)2 + 64
∴ 100 = x2 − 2x + 1 + 64
∴ 100 = x2 − 2x + 65
∴ x2 − 2x + 65 − 100 = 0
∴ x2 − 2x − 35 = 0
∴ x2 − 7x + 5x - 35 = 0
∴ x(x − 7) + 5(x − 7) = 0
∴ (x − 7)(x + 5) = 0
∴ x − 7 = 0 or x + 5 = 0
∴ x = 7 or x = −5
x = 7 or x = −5
APPEARS IN
संबंधित प्रश्न
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(4, 5), (7, 6), (4, 3), (1, 2)
The value of 'a' for which of the following points A(a, 3), B (2, 1) and C(5, a) a collinear. Hence find the equation of the line.
Find the values of x, y if the distances of the point (x, y) from (-3, 0) as well as from (3, 0) are 4.
Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Determine whether the point is collinear.
R(0, 3), D(2, 1), S(3, –1)
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
Find the distance of a point (13 , -9) from another point on the line y = 0 whose abscissa is 1.
Find the point on the x-axis equidistant from the points (5,4) and (-2,3).
Find the distance between the points (a, b) and (−a, −b).
Find the distance between the origin and the point:
(-8, 6)
Find the coordinates of the points on the y-axis, which are at a distance of 10 units from the point (-8, 4).
Prove that the points A (1, -3), B (-3, 0) and C (4, 1) are the vertices of an isosceles right-angled triangle. Find the area of the triangle.
Show that (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.
Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.
The distance of the point P(–6, 8) from the origin is ______.
The point P(–2, 4) lies on a circle of radius 6 and centre C(3, 5).
Find the distance between the points O(0, 0) and P(3, 4).
The distance between the points (0, 5) and (–3, 1) is ______.
|
Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players is represented as points on a coordinate plane. |
- At an instance, the midfielders and forward formed a parallelogram. Find the position of the central midfielder (D) if the position of other players who formed the parallelogram are :- A(1, 2), B(4, 3) and C(6, 6)
- Check if the Goal keeper G(–3, 5), Sweeper H(3, 1) and Wing-back K(0, 3) fall on a same straight line.
[or]
Check if the Full-back J(5, –3) and centre-back I(–4, 6) are equidistant from forward C(0, 1) and if C is the mid-point of IJ. - If Defensive midfielder A(1, 4), Attacking midfielder B(2, –3) and Striker E(a, b) lie on the same straight line and B is equidistant from A and E, find the position of E.
