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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 the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that bx = ay.
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
Find the distance between the following pair of points:
(–6, 7) and (–1, –5)
Find the distance between the points:
A(–6, –4) and B(9, –12)
A(-2, -3), B(-1, 0) and C(7, -6) are the vertices of a triangle. Find the circumcentre and the circumradius of the triangle.
Prove that the points (0 , 2) , (1 , 1) , (4 , 4) and (3 , 5) are the vertices of a rectangle.
A(2, 5), B(-2, 4) and C(-2, 6) are the vertices of a triangle ABC. Prove that ABC is an isosceles triangle.
Find the distance between the points (a, b) and (−a, −b).
Find the distance between the following pairs of points:
(–3, 6) and (2, –6)
Find the distance between the origin and the point:
(8, −15)
Find the distance of the following points from origin.
(a+b, a-b)
Find distance between point Q(3, –7) and point R(3, 3)
Solution: Suppose Q(x1, y1) and point R(x2, y2)
x1 = 3, y1 = –7 and x2 = 3, y2 = 3
Using distance formula,
d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `sqrt(square - 100)`
∴ d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `square`
The distance between the points (0, 5) and (–5, 0) is ______.
A circle drawn with origin as the centre passes through `(13/2, 0)`. The point which does not lie in the interior of the circle 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 ______.
The distance between the points A(0, 6) and B(0, –2) is ______.
∆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).
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.
What is the distance of the point (– 5, 4) from the origin?
