Advertisements
Advertisements
Question
Find distance of point A(6, 8) from origin.
Advertisements
Solution
Let A(x1, y1) = A(6, 8), O(x2, y2) = O(0, 0)
∴ x1 = 6, y1 = 8, x2 = 0, y2 = 0
By distance formula,
d(A, O) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt((0 - 6)^2 + (0 - 8)^2`
= `sqrt(36 + 64)`
= `sqrt(100)`
= 10
∴ The distance of point A(6, 8) from origin is 10 units.
APPEARS IN
RELATED QUESTIONS
If P (2, – 1), Q(3, 4), R(–2, 3) and S(–3, –2) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus
Find the distance between the following pairs of points:
(2, 3), (4, 1)
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 distance QR and PR.
Find the value of a when the distance between the points (3, a) and (4, 1) is `sqrt10`
If the points (2, 1) and (1, -2) are equidistant from the point (x, y), show that x + 3y = 0.
Using the distance formula, show that the given points are collinear:
(-2, 5), (0,1) and (2, -3)
If P (x , y ) is equidistant from the points A (7,1) and B (3,5) find the relation between x and y
Find the distance between the following point :
(p+q,p-q) and (p-q, p-q)
Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.
Find the relation between a and b if the point P(a ,b) is equidistant from A (6,-1) and B (5 , 8).
Prove that the points (1 , 1) , (-1 , -1) and (`- sqrt 3 , sqrt 3`) are the vertices of an equilateral triangle.
Given A = (3, 1) and B = (0, y - 1). Find y if AB = 5.
Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).
Find distance between point A(–1, 1) and point B(5, –7):
Solution: Suppose A(x1, y1) and B(x2, y2)
x1 = –1, y1 = 1 and x2 = 5, y2 = –7
Using distance formula,
d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
∴ d(A, B) = `sqrt(square +[(-7) + square]^2`
∴ d(A, B) = `sqrt(square)`
∴ d(A, B) = `square`
The distance between the points A(0, 6) and B(0, -2) 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 points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
