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प्रश्न
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`
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उत्तर
Suppose Q(x1, y1) and point R(x2, y2)
x1 = 3, y1 = –7 and x2 = 3, y2 = 3
Using distance formula,
d(Q, R) = \[\sqrt{\boxed{(x_2 - x_1)^2 + (y_2 - y_1)^2}}\]
= `sqrt((3 - 3)^2 - [3 - (- 7)]^2`
= `sqrt(0^2 + (10)^2)`
∴ d(Q, R) = \[\sqrt{\boxed{0} - 100}\]
∴ d(Q, R) = \[\sqrt{\boxed{100}}\]
∴ d(Q, R) = \[\boxed{10}\]
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संबंधित प्रश्न
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.
Using distance formula, find which of them is correct.

Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(4, 5), (7, 6), (4, 3), (1, 2)
Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.
If the points (2, 1) and (1, -2) are equidistant from the point (x, y), show that x + 3y = 0.
Find the values of x, y if the distances of the point (x, y) from (-3, 0) as well as from (3, 0) are 4.
Find the distance between the points:
P(a + b, a - b) and Q(a - b, a + b)
Find the distance of the following points from the origin:
(iii) C (-4,-6)
Find the distances between the following point.
P(–6, –3), Q(–1, 9)
Find the distance of the following point from the origin :
(5 , 12)
Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.
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.
The distance between the points (3, 1) and (0, x) is 5. Find x.
Points A (-3, -2), B (-6, a), C (-3, -4) and D (0, -1) are the vertices of quadrilateral ABCD; find a if 'a' is negative and AB = CD.
The distance between points P(–1, 1) and Q(5, –7) is ______.
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 distance between the points (0, 5) and (–5, 0) 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 ______.
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
What is the distance of the point (– 5, 4) from the origin?
Find the distance between the points O(0, 0) and P(3, 4).
