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प्रश्न
Find the distance between the following pairs of points:
(−5, 7), (−1, 3)
Find the distance between the following pairs of points:
P(-5, 7), Q(-1, 3)
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उत्तर १
Distance between (−5, 7) and (−1, 3) is given by
l = `sqrt((x_2-x_1)^2+(y_2-y_1)^2)`
l = `sqrt((-5-(-1))^2 + (7 -3)^2)`
= `sqrt((-4)^2+(4)^2)`
= `sqrt(16+16) `
= `sqrt32`
= `4sqrt2` units
उत्तर २
Let the co-ordinates of point P are (x1, y1) and of point Q are (x2, y2)
P(–5, 7) = (x1, y1)
Q(–1, 3) = (x2, y2)
PQ = `sqrt((x_2-x_1)^2+(y_2-y_1)^2)` ...(By distance formula)
= `sqrt((-1-(-5))^2+(3-7)^2)`
= `sqrt((-1+5)^2+(-4)^2)`
= `sqrt(4^2+16)`
= `sqrt(16 + 16)`
= `sqrt32`
= `sqrt(16xx2)`
= `sqrt16xxsqrt2`
= 4`sqrt2` units
संबंधित प्रश्न
If A(4, 3), B(-1, y) and C(3, 4) are the vertices of a right triangle ABC, right-angled at A, then find the value of y.
If two vertices of an equilateral triangle be (0, 0), (3, √3 ), find the third vertex
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)
If Q (0, 1) is equidistant from P (5, –3) and R (x, 6), find the values of x. Also, find the distances QR and PR.
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.
Two opposite vertices of a square are (–1, 2) and (3, 2). Find the coordinates of other two vertices.
A(–8, 0), B(0, 16) and C(0, 0) are the vertices of a triangle ABC. Point P lies on AB and Q lies on AC such that AP : PB = 3 : 5 and AQ : QC = 3 : 5. Show that : PQ = `3/8` BC.
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
Find the distance between the following point :
(sec θ , tan θ) and (- tan θ , sec θ)
Find the relation between a and b if the point P(a ,b) is equidistant from A (6,-1) and B (5 , 8).
Find the coordinate of O , the centre of a circle passing through P (3 , 0), Q (2 , `sqrt 5`) and R (`-2 sqrt 2` , -1). Also find its radius.
Find the coordinates of O, the centre passing through A( -2, -3), B(-1, 0) and C(7, 6). Also, find its radius.
Prove that the points (1 ,1),(-4 , 4) and (4 , 6) are the certices of an isosceles triangle.
Prove that the points (1 , 1) , (-1 , -1) and (`- sqrt 3 , sqrt 3`) are the vertices of an equilateral triangle.
Find distance of point A(6, 8) from origin.
The distance of the point (α, β) from the origin 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 ______.
Find the points on the x-axis which are at a distance of `2sqrt(5)` from the point (7, – 4). How many such points are there?
Find distance between points P(– 5, – 7) and Q(0, 3).
By distance formula,
PQ = `sqrt(square + (y_2 - y_1)^2`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(125)`
= `5sqrt(5)`
The distance between the points (0, 5) and (–3, 1) is ______.
