Advertisements
Advertisements
Question
If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x.
Advertisements
Solution
Let L(x1, y1) = L(x, 7) and M(x2, y2) = M(1, 15)
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.
APPEARS IN
RELATED QUESTIONS
If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
If the points (2, 1) and (1, -2) are equidistant from the point (x, y), show that x + 3y = 0.
Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Find all possible values of y for which distance between the points is 10 units.
Find x if distance between points L(x, 7) and M(1, 15) is 10.
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
Find the distance of the following point from the origin :
(13 , 0)
Find the relation between x and y if the point M (x,y) is equidistant from R (0,9) and T (14 , 11).
Find the point on the x-axis equidistant from the points (5,4) and (-2,3).
Find the coordinate of O , the centre of a circle passing through P (3 , 0), Q (2 , `sqrt 5`) and R (`-2 sqrt 2` , -1). Also find its radius.
The centre of a circle passing through P(8, 5) is (x+l , x-4). Find the coordinates of the centre if the diameter of the circle is 20 units.
Find the distance between the following pair of points:
`(sqrt(3)+1,1)` and `(0, sqrt(3))`
Find the distance between the origin and the point:
(-8, 6)
A point P (2, -1) is equidistant from the points (a, 7) and (-3, a). Find a.
What point on the x-axis is equidistant from the points (7, 6) and (-3, 4)?
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x = ______.
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:
What are the coordinates of the position of a player Q such that his distance from K is twice his distance from E and K, Q and E are collinear?
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.
Show that Alia's house, Shagun's house and library for an isosceles right triangle.
