Advertisements
Advertisements
प्रश्न
Find the distance between the points O(0, 0) and P(3, 4).
Advertisements
उत्तर
O(0, 0), P(3, 4)
∴ `(x_1, y_1) = (0, 0)`
`(x_2, y_2) = (3, 4)`
∴ `x_1=0, y_1= 0`
`x_2 = 3, y_2 = 4`
d(OP) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt((3 - 0)^2 + (4 - 0)^2`
= `sqrt((3)^2 + (4)^2)`
= `sqrt(9 + 16)`
= `sqrt(25)`
d(OP) = 5 units
APPEARS IN
संबंधित प्रश्न
Find the distance between two points
(i) P(–6, 7) and Q(–1, –5)
(ii) R(a + b, a – b) and S(a – b, –a – b)
(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`
Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
Find the distance between the following pair of points:
(–6, 7) and (–1, –5)
The length of a line segment is of 10 units and the coordinates of one end-point are (2, –3). If the abscissa of the other end is 10, find the ordinate of the other end.
Prove that the points A(1, 7), B(4, 2), C(−1, −1), and D(−4, 4) are the vertices of a square.
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.
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 values of x for which the distance between the points P(x, 4) and Q(9, 10) is 10 units.
Find the distance of a point (13 , -9) from another point on the line y = 0 whose abscissa is 1.
Prove that the following set of point is collinear :
(4, -5),(1 , 1),(-2 , 7)
P(5 , -8) , Q (2 , -9) and R(2 , 1) are the vertices of a triangle. Find tyhe circumcentre and the circumradius of the triangle.
Find the distance between the following pairs of points:
`(3/5,2) and (-(1)/(5),1(2)/(5))`
Find the distance between the following pair of points:
`(sqrt(3)+1,1)` and `(0, sqrt(3))`
A point A is at a distance of `sqrt(10)` unit from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice its abscissa.
A point P (2, -1) is equidistant from the points (a, 7) and (-3, a). Find a.
Show that (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.
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 between the points A(0, 6) and B(0, –2) is ______.
Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?
