Advertisements
Advertisements
प्रश्न
If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x.
Advertisements
उत्तर
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
संबंधित प्रश्न
If P and Q are two points whose coordinates are (at2 ,2at) and (a/t2 , 2a/t) respectively and S is the point (a, 0). Show that `\frac{1}{SP}+\frac{1}{SQ}` is independent of t.
Find the coordinates of the centre of the circle passing through the points (0, 0), (–2, 1) and (–3, 2). Also, find its radius.
Find the distance between the following pairs of points:
(2, 3), (4, 1)
If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.
Find all possible values of y for which distance between the points is 10 units.
Find the distance between the following pair of point in the coordinate plane :
(5 , -2) and (1 , 5)
ABC is an equilateral triangle . If the coordinates of A and B are (1 , 1) and (- 1 , -1) , find the coordinates of C.
Find the distance between the origin and the point:
(-5, -12)
Find the co-ordinates of points on the x-axis which are at a distance of 17 units from the point (11, -8).
A point A is at a distance of `sqrt(10)` unit from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice its abscissa.
Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).
Calculate the distance between the points P (2, 2) and Q (5, 4) correct to three significant figures.
By using the distance formula prove that each of the following sets of points are the vertices of a right angled triangle.
(i) (6, 2), (3, -1) and (- 2, 4)
(ii) (-2, 2), (8, -2) and (-4, -3).
Show that the points (a, a), (-a, -a) and `(-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.
Find distance of point A(6, 8) from origin.
Seg OA is the radius of a circle with centre O. The coordinates of point A is (0, 2) then decide whether the point B(1, 2) is on the circle?
The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
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 ______.
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:
The point on y axis equidistant from B and C is ______.
Find the points on the x-axis which are at a distance of `2sqrt(5)` from the point (7, – 4). How many such points are there?
