Advertisements
Advertisements
प्रश्न
If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______
पर्याय
7
7 or – 5
–1
1
Advertisements
उत्तर
7 or – 5
Here, x1 = x, y1 = 7, x2 = 1, y2 = 15
By distance formula,
d(L, M) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
∴ d(L, M) = `sqrt((1 - x)^2 + (15 - 7)^2)`
∴ 10 = `sqrt((1 - x)^2 + 8^2)`
∴ 100 = (1 - x)2 + 64 ...[Squaring both sides]
∴ (1 - x)2 = 100 - 64
∴ (1 - x)2 = 36
∴ 1 - x = `+-sqrt(36)` ...[Taking square root of both sides]
∴ 1 - x = `+-6`
∴ 1 - x = 6 or 1 - x = -6
∴ x = -5 or x = 7
∴ The value of x is -5 or 7.
संबंधित प्रश्न
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
If two vertices of an equilateral triangle be (0, 0), (3, √3 ), find the third vertex
Find the distance between the following pair of points:
(a+b, b+c) and (a-b, c-b)
Given a triangle ABC in which A = (4, −4), B = (0, 5) and C = (5, 10). A point P lies on BC such that BP : PC = 3 : 2. Find the length of line segment AP.
`" Find the distance between the points" A ((-8)/5,2) and B (2/5,2)`
Find the distance between the following pair of point.
P(–5, 7), Q(–1, 3)
Find the distance between the following pair of point in the coordinate plane :
(5 , -2) and (1 , 5)
Find the distance between the following point :
(sin θ , cos θ) and (cos θ , - sin θ)
Find the coordinate of O , the centre of a circle passing through A (8 , 12) , B (11 , 3), and C (0 , 14). Also , find its radius.
Prove that the points (a, b), (a + 3, b + 4), (a − 1, b + 7) and (a − 4, b + 3) are the vertices of a parallelogram.
In what ratio does the point P(−4, y) divides the line segment joining the points A(−6, 10) and B(3, −8)? Hence find the value of y.
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the ordinate of point P.
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the abscissa of point Q.
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT
Show that each of the triangles whose vertices are given below are isosceles :
(i) (8, 2), (5,-3) and (0,0)
(ii) (0,6), (-5, 3) and (3,1).
Find distance between point Q(3, – 7) and point R(3, 3)
Solution: Suppose Q(x1, y1) and point R(x2, y2)
x1 = 3, y1 = – 7 and x2 = 3, y2 = 3
Using distance formula,
d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `sqrt(square - 100)`
∴ d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `square`
Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -
- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
Using the picture of a hockey field below, answer the questions that follow:
If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by ______.
The point P(–2, 4) lies on a circle of radius 6 and centre C(3, 5).
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
