Advertisements
Advertisements
प्रश्न
Find x if distance between points L(x, 7) and M(1, 15) is 10.
Advertisements
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
If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.
If the opposite vertices of a square are (1, – 1) and (3, 4), find the coordinates of the remaining angular points.
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
Prove that the points A(1, 7), B(4, 2), C(−1, −1), and D(−4, 4) are the vertices of a square.
An equilateral triangle has two vertices at the points (3, 4) and (−2, 3), find the coordinates of the third vertex.
Find the distance of the following points from the origin:
A(5, –12)
Find all possible values of x for which the distance between the points A(x, –1) and B(5, 3) is 5 units.
Find the distance between the following pair of points.
R(0, -3), S(0, `5/2`)
PQR is an isosceles triangle . If two of its vertices are P (2 , 0) and Q (2 , 5) , find the coordinates of R if the length of each of the two equal sides is 3.
Find the distance between the points (a, b) and (−a, −b).
Find the distance between the following pair of points:
`(sqrt(3)+1,1)` and `(0, sqrt(3))`
Use distance formula to show that the points A(-1, 2), B(2, 5) and C(-5, -2) are collinear.
Show that the points (a, a), (-a, -a) and `(-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.
The distance of the point P(–6, 8) from the origin is ______.
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?
The point P(–2, 4) lies on a circle of radius 6 and centre C(3, 5).
If the point A(2, – 4) is equidistant from P(3, 8) and Q(–10, y), find the values of y. Also find distance PQ.
If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.
|
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.
