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प्रश्न
The distance between points P(–1, 1) and Q(5, –7) is ______
विकल्प
11 cm
10 cm
5 cm
7 cm
उत्तर
10 cm
Let P(x1, y1) = P( -1, 1) and Q(x2, y2) = Q(5, -7)
Here, x1 = -1, y1 = 1, x2 = 5, y2 = -7
By distance formula,
d(P, Q) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
∴ d(P, Q) = `sqrt([5 - (-1)]^2 + (-7- 1)^2)`
∴ d(P, Q) = `sqrt(36 + 64)`
∴ d(P, Q) = `sqrt(100)`
∴ d(P, Q) = 10 cm
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संबंधित प्रश्न
Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.
Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.
Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle
Find the distance of the following points from the origin:
(i) A(5,- 12)
Using the distance formula, show that the given points are collinear:
(1, -1), (5, 2) and (9, 5)
Find the distance between the following pair of point.
P(–5, 7), Q(–1, 3)
Find the distance between the following point :
(p+q,p-q) and (p-q, p-q)
Prove that the points (5 , 3) , (1 , 2), (2 , -2) and (6 ,-1) are the vertices of a square.
ABCD is a square . If the coordinates of A and C are (5 , 4) and (-1 , 6) ; find the coordinates of B and D.
Find the distance between the origin and the point:
(-8, 6)
Find the distance between the origin and the point:
(-5, -12)
Given A = (3, 1) and B = (0, y - 1). Find y if AB = 5.
Show that the point (11, – 2) is equidistant from (4, – 3) and (6, 3)
If the distance between the points (4, P) and (1, 0) is 5, then the value of p 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 ______.
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
∆ABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to ∆DEF with vertices D(–4, 0), E(4, 0) and F(0, 4).
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
The distance of the point (5, 0) from the origin is ______.
