Advertisements
Advertisements
Question
Find the distance between the origin and the point:
(8, −15)
Advertisements
Solution
Coordinates of origin are O (0, 0).
C (8, −15)
CO = `sqrt((0 - 8)^2 + (0 + 15)^2)`
= `sqrt(64 + 225)`
= `sqrt(289)`
= 17
APPEARS IN
RELATED QUESTIONS
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 circumcenter of the triangle whose vertices are (-2, -3), (-1, 0), (7, -6).
Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two
vertices.
Prove that the following set of point is collinear :
(5 , 5),(3 , 4),(-7 , -1)
Prove that the following set of point is collinear :
(5 , 1),(3 , 2),(1 , 3)
The distance between the point P(1, 4) and Q(4, 0) is ______.
The distance of the point (α, β) from the origin is ______.
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 (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.
