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प्रश्न
Find the distance of the following point from the origin :
(6 , 8)
उत्तर
P = (0 , 0) Q = (6 , 8)
PQ = `sqrt ((6 - 0)^2 + (8 - 0)^2)`
`= sqrt (36 + 64)`
`= sqrt 100`
= 10 units
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संबंधित प्रश्न
Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
Find the distance of a point (7 , 5) from another point on the x - axis whose abscissa is -5.
Prove that the following set of point is collinear :
(5 , 1),(3 , 2),(1 , 3)
Find the distance between the following pairs of points:
(-3, 6) and (2, -6)
Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x ______
Find distance between point A(–1, 1) and point B(5, –7):
Solution: Suppose A(x1, y1) and B(x2, y2)
x1 = –1, y1 = 1 and x2 = 5, y2 = – 7
Using distance formula,
d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
∴ d(A, B) = `sqrt(square +[(-7) + square]^2`
∴ d(A, B) = `sqrt(square)`
∴ d(A, B) = `square`
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 coordinates of the centroid of ΔEHJ are ______.
Show that Alia's house, Shagun's house and library for an isosceles right triangle.
