Advertisements
Advertisements
Question
From the given number line, find d(A, B):
Advertisements
Solution
Distance formula = (x2 – x1)
d(A, B) = 3 – (–3)
= 3 + 3
= 6 units.
APPEARS IN
RELATED QUESTIONS
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(4, 5), (7, 6), (4, 3), (1, 2)
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.
If a≠b≠0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.
Prove that the points A(1, 7), B (4, 2), C(−1, −1) D (−4, 4) are the vertices of a square.
Find all possible values of x for which the distance between the points
A(x,-1) and B(5,3) is 5 units.
Find value of x for which the distance between the points P(x,4) and Q(9,10) is 10 units.
Find the distance between the following pair of points.
L(5, –8), M(–7, –3)
Find the distance between the following pairs of point.
W `((- 7)/2 , 4)`, X (11, 4)
Find the distance between the following pair of point in the coordinate plane :
(5 , -2) and (1 , 5)
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
Find the distance of the following point from the origin :
(13 , 0)
Find the distance of a point (13 , -9) from another point on the line y = 0 whose abscissa is 1.
Find the point on the x-axis equidistant from the points (5,4) and (-2,3).
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
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.
If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, 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:
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?
The point P(–2, 4) lies on a circle of radius 6 and centre C(3, 5).
Show that points A(–1, –1), B(0, 1), C(1, 3) are collinear.
