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प्रश्न
Find distance between point A(7, 5) and B(2, 5).
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उत्तर
Let A(x1, y1) = A(7, 5) and B(x2, y2) = B(2, 5)
∴ By distance formula,
d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt((2 - 7)^2 + (5 - 5)^2`
= `sqrt((-5)^2 + 0^2)`
= `sqrt(25)`
= 5 cm
∴ The distance between points A and B is 5 cm.
संबंधित प्रश्न
Find the distance between the following pairs of points:
(2, 3), (4, 1)
Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.
Given a line segment AB joining the points A(–4, 6) and B(8, –3). Find
1) The ratio in which AB is divided by y-axis.
2) Find the coordinates of the point of intersection.
3) The length of AB.
Find the value of a when the distance between the points (3, a) and (4, 1) is `sqrt10`
Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Find all possible values of y for which the distance between the points A(2, –3) and B(10, y) is 10 units.
If the point A(x, 2) is equidistant from the points B(8, –2) and C(2, –2), find the value of x. Also, find the length of AB.
Find the relation between a and b if the point P(a ,b) is equidistant from A (6,-1) and B (5 , 8).
The centre of a circle passing through P(8, 5) is (x+l , x-4). Find the coordinates of the centre if the diameter of the circle is 20 units.
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
Prove that the points (0 , 0) , (3 , 2) , (7 , 7) and (4 , 5) are the vertices of a parallelogram.
Find the distance between the following pairs of points:
(–3, 6) and (2, –6)
Find the distance between the origin and the point:
(-5, -12)
What point on the x-axis is equidistant from the points (7, 6) and (-3, 4)?
Find distance of point A(6, 8) from origin.
Show that the points (0, –1), (8, 3), (6, 7) and (–2, 3) are vertices of a rectangle.
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 distance of the point P(–6, 8) from the origin is ______.
What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?
The distance between the points (0, 5) and (–3, 1) is ______.
