Advertisements
Advertisements
Question
Find the distance between the points
A(1,-3) and B(4,-6)
Advertisements
Solution
A(1,-3) and B(4,-6)
The given points are A(1,-3) and B(4,-6 )
`Then (x_1 =1,y_1=-3) and (x_2 = 4, y_2=-6)`
`AB = sqrt((x_2-x_1)^2 +(y_2-y_1)^2)`
`=sqrt((4-1)^2+{-6-(-3)}^2)`
`=sqrt((4-1)^2 + (-6+3)^2)`
`= sqrt((3)^2 +(-3)^2`
`= sqrt(9+9)`
`=sqrt(18)`
`=sqrt(9xx2)`
`=3 sqrt(2) ` units
APPEARS IN
RELATED QUESTIONS
Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle
Find the distance between the following pairs of points:
(a, b), (−a, −b)
Given a line segment AB joining the points A(–4, 6) and B(8, –3). Find
1) The ratio in which AB is divided by y-axis.
2) Find the coordinates of the point of intersection.
3) The length of AB.
Prove that the points A(1, 7), B (4, 2), C(−1, −1) D (−4, 4) are the vertices of a square.
The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) ?
Find the distances between the following point.
P(–6, –3), Q(–1, 9)
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then ______.
Find the distance between the following pair of point in the coordinate plane.
(1 , 3) and (3 , 9)
ABCD is a square . If the coordinates of A and C are (5 , 4) and (-1 , 6) ; find the coordinates of B and D.
Find the distance between the origin and the point:
(8, −15)
Prove that the points P (0, -4), Q (6, 2), R (3, 5) and S (-3, -1) are the vertices of a rectangle PQRS.
The distance between points P(–1, 1) and Q(5, –7) is ______
Show that the point (0, 9) is equidistant from the points (– 4, 1) and (4, 1)
The distance between the points (0, 5) and (–5, 0) is ______.
The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is ______.
The distance of the point (α, β) from the origin 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:
What are the coordinates of the position of a player Q such that his distance from K is twice his distance from E and K, Q and E are collinear?
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 points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
