Advertisements
Advertisements
Question
Find the distance between the points O(0, 0) and P(3, 4).
Advertisements
Solution
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
RELATED QUESTIONS
Find the distance between the following pairs of points:
(−5, 7), (−1, 3)
Find the distance between the following pair of points:
(asinα, −bcosα) and (−acos α, bsin α)
Find the circumcenter of the triangle whose vertices are (-2, -3), (-1, 0), (7, -6).
`" Find the distance between the points" A ((-8)/5,2) and B (2/5,2)`
For what values of k are the points (8, 1), (3, –2k) and (k, –5) collinear ?
Find the distance between the following pair of points.
R(0, -3), S(0, `5/2`)
Find x if distance between points L(x, 7) and M(1, 15) is 10.
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then ______.
Find the value of a if the distance between the points (5 , a) and (1 , 5) is 5 units .
Prove that the points (0 , 2) , (1 , 1) , (4 , 4) and (3 , 5) are the vertices of a rectangle.
Find the distance between the origin and the point:
(-8, 6)
Find distance CD where C(– 3a, a), D(a, – 2a)
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
The coordinates of the point which is equidistant from the three vertices of the ΔAOB as shown in the figure 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 ______.
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 point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
