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प्रश्न
Find the distance between the following pairs of points:
(2, 3), (4, 1)
Find the distance between the following pairs of points:
A (2, 3), B (4, 1)
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उत्तर १
l = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
= `sqrt((4 - 2)^2 + (1 - 3)^2)`
= `sqrt(2^2 + (- 2)^2)`
= `sqrt(4 + 4)`
= `sqrt(8)`
= `sqrt(4 × 2)`
= `2sqrt(2)` units
उत्तर २
A (2, 3), B (4, 1)
Suppose the coordinates of point A are (x1, y1) and those of point B are (x2, y2).
x1 = 2, y1 = 3, x2 = 4, y2 = 1
According to distance formula,
d(A,B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
d(A,B) = `sqrt((4 - 2)^2 + (1 - 3)^2)`
d(A,B) = `sqrt(2^2 + (- 2)^2)`
d(A,B) = `sqrt(4 + 4)`
d(A,B) = `sqrt(8)`
d(A,B) = `sqrt(4 × 2)`
d(A,B) = `2sqrt(2)`
The distance between points A and B is `2sqrt(2)` units.
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.
Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.
If the point P(x, y ) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.
Find the distance of the following points from the origin:
C(–4, –6)
Determine whether the points are collinear.
L(–2, 3), M(1, –3), N(5, 4)
Find the distances between the following point.
R(–3a, a), S(a, –2a)
AB and AC are the two chords of a circle whose radius is r. If p and q are
the distance of chord AB and CD, from the centre respectively and if
AB = 2AC then proove that 4q2 = p2 + 3r2.
Distance of point (−3, 4) from the origin is ______.
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then ______.
Find the value of a if the distance between the points (5 , a) and (1 , 5) is 5 units .
Prove that the following set of point is collinear :
(5 , 1),(3 , 2),(1 , 3)
Prove that the points (6 , -1) , (5 , 8) and (1 , 3) are the vertices of an isosceles triangle.
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
ABC is an equilateral triangle . If the coordinates of A and B are (1 , 1) and (- 1 , -1) , find the coordinates of C.
Given A = (x + 2, -2) and B (11, 6). Find x if AB = 17.
The distance between points P(–1, 1) and Q(5, –7) 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 point on y axis equidistant from B and C is ______.
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Case Study Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. |
- Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
- After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?
The distance of the point (5, 0) from the origin is ______.
