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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 the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.
Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.
Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle
Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3)
If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.
Find the distance between the points:
A(9, 3) and B(15, 11)
Find the distance between the points:
A(1, –3) and B(4, –6)
Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle.
Find the value of y for which the distance between the points A (3, −1) and B (11, y) is 10 units.
Find the distance between the following point :
(sec θ , tan θ) and (- tan θ , sec θ)
Find the coordinates of O, the centre passing through A( -2, -3), B(-1, 0) and C(7, 6). Also, find its radius.
x (1,2),Y (3, -4) and z (5,-6) are the vertices of a triangle . Find the circumcentre and the circumradius of the triangle.
Prove that the points A (1, -3), B (-3, 0) and C (4, 1) are the vertices of an isosceles right-angled triangle. Find the area of the triangle.
Use distance formula to show that the points A(-1, 2), B(2, 5) and C(-5, -2) are collinear.
If the point (x, y) is at equidistant from the point (a + b, b – a) and (a-b, a + b). Prove that ay = bx.
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 ______.
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?
The distance between the points (0, 5) and (–3, 1) is ______.
