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प्रश्न
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x ______
विकल्प
2
6
3
1
उत्तर
6
Let P(x1, y1) = P( 2, 2) and Q(x2, y2) = Q(5, x)
Here, x1 = 2, y1 = 2, x2 = 5, y2 = x
By distance formula,
d(P, Q) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
∴ 5 = `sqrt((5 - 2)^2 + (x - 2)^2)`
∴ 5 = `sqrt(9 + x^2 - 4x + 4)`
∴ 52 = x2 - 4x + 13 ...[Squaring both sides]
∴ 25 = x2 - 4x + 13
∴ x2 - 4x + 13 - 25 = 0
∴ x2 - 4x - 12 = 0
∴ (x - 6) (x + 2) = 0
∴ x - 6 = 0 or x + 2 = 0
∴ x = 6 or x = -2
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संबंधित प्रश्न
Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle.
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
Find the distance between the following pair of point in the coordinate plane :
(5 , -2) and (1 , 5)
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(p+q,p-q) and (p-q, p-q)
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(sin θ , cos θ) and (cos θ , - sin θ)
Find the distance between the following point :
(sec θ , tan θ) and (- tan θ , sec θ)
Find the value of m if the distance between the points (m , -4) and (3 , 2) is 3`sqrt 5` units.
Prove that the following set of point is collinear :
(5 , 1),(3 , 2),(1 , 3)
Prove that the points (a, b), (a + 3, b + 4), (a − 1, b + 7) and (a − 4, b + 3) are the vertices of a parallelogram.
Find the distance between the origin and the point:
(8, -15)
The distance between the points (3, 1) and (0, x) is 5. Find x.
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Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
Find distance between point A(– 3, 4) and origin O
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x 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:
The coordinates of the centroid of ΔEHJ are ______.
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 x axis equidistant from I and E is ______.
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
The distance between the points (0, 5) and (–3, 1) is ______.
