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प्रश्न
Find the co-ordinates of points on the x-axis which are at a distance of 17 units from the point (11, -8).
उत्तर
Let the coordinates of the point on x-axis be (x, 0).
From the given information, we have:
`sqrt((x -11)^2 + (0 + 8)^2)` = 17
(x - 11)2 + (0 + 8)2 = 289
x2 + 121 - 22x + 64 = 289
x2 - 22x - 104 = 0
x2 - 26x + 4x - 104 = 0
x(x - 26) + 4(x - 26) = 0
(x - 26)(x + 4) = 0
x = 26, -4
Thus, the required co-ordinates of the points on x-axis are (26, 0) and (-4, 0).
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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 the opposite vertices of a square are (1, – 1) and (3, 4), find the coordinates of the remaining angular points.
Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
Given a line segment AB joining the points A(–4, 6) and B(8, –3). Find
1) The ratio in which AB is divided by y-axis.
2) Find the coordinates of the point of intersection.
3) The length of AB.
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)`
Distance of point (-3, 4) from the origin is .....
(A) 7 (B) 1 (C) 5 (D) 4
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
Prove that the points (7 , 10) , (-2 , 5) and (3 , -4) are vertices of an isosceles right angled triangle.
Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.
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.
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.
Calculate the distance between A (5, -3) and B on the y-axis whose ordinate is 9.
Find the distance of the following points from origin.
(5, 6)
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).
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.
The equation of the perpendicular bisector of line segment joining points A(4,5) and B(-2,3) is ______.
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 ______.
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?
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
