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प्रश्न
The distance of the point P(–6, 8) from the origin is ______.
विकल्प
8
`2sqrt(7)`
10
6
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उत्तर
The distance of the point P(–6, 8) from the origin is 10.
Explanation:
Distance formula: d2 = (x2 – x1)2 + (y2 – y1)2
According to the question,
We have,
x1 = – 6, x2 = 0
y1 = 8, y2 = 0
d2 = [0 – (– 6)]2 + [0 – 8]2
d = `sqrt((0 - (-6))^2 + (0 - 8)^2`
d = `sqrt((6)^2 + (-8)^2`
d = `sqrt(36 + 64)`
d = `sqrt(100)`
d = 10
Therefore, the distance between P(–6, 8) and origin O(0, 0) is 10.
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संबंधित प्रश्न
Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area
Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3)
Find the distance between the points
(i) A(9,3) and B(15,11)
Find the distance between the following pair of point in the coordinate plane.
(1 , 3) and (3 , 9)
Find the distance of the following point from the origin :
(0 , 11)
Prove that the points (0,3) , (4,3) and `(2, 3+2sqrt 3)` are the vertices of an equilateral triangle.
Show that the points (2, 0), (–2, 0), and (0, 2) are the vertices of a triangle. Also, a state with the reason for the type of triangle.
A point P (2, -1) is equidistant from the points (a, 7) and (-3, a). Find a.
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT
Calculate the distance between A (5, -3) and B on the y-axis whose ordinate is 9.
The points A (3, 0), B (a, -2) and C (4, -1) are the vertices of triangle ABC right angled at vertex A. Find the value of a.
Show that the quadrilateral with vertices (3, 2), (0, 5), (- 3, 2) and (0, -1) is a square.
Find distance between point A(–3, 4) and origin O.
If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x.
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x 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 coordinates of the centroid of ΔEHJ are ______.
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.
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.
