Advertisements
Advertisements
Question
Find all possible values of y for which distance between the points is 10 units.
Advertisements
Solution
The given points are A(2,-3) and B(10, y)
`∴AB = sqrt((2-10)^2 +(-3-y)^2)`
`=sqrt((-8)^2 + (-3-y)^2)`
`=sqrt(64+9+y^2+6y)`
∵ AB= 10
`∴sqrt(64+9+y^2+6y =10)`
`⇒ 73+y^2+6y =100` (Squaring both sides)
`⇒y^2+6y-27 = 0`
`⇒y^2+9y -3y-27=0`
`⇒ y(y+9)-3(y+9)=0`
`⇒(y+9)(y-3)=0`
⇒y+9=0 or y-3=0
⇒ y=-9 or y=3
Hence, the possible values of y are -9 and 3.
APPEARS IN
RELATED QUESTIONS
If the point P(2, 2) is equidistant from the points A(−2, k) and B(−2k, −3), find k. Also find the length of AP.
Find the distance between two points
(i) P(–6, 7) and Q(–1, –5)
(ii) R(a + b, a – b) and S(a – b, –a – b)
(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`
Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.
If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?
Find the distance of a point P(x, y) from the origin.
Find the distance between the following pairs of point.
W `((- 7)/2 , 4)`, X (11, 4)
Find the distance of the following point from the origin :
(6 , 8)
Find the distance between P and Q if P lies on the y - axis and has an ordinate 5 while Q lies on the x - axis and has an abscissa 12 .
Find the point on the x-axis equidistant from the points (5,4) and (-2,3).
From the given number line, find d(A, B):
Calculate the distance between A (5, -3) and B on the y-axis whose ordinate is 9.
Find the distance of the following points from origin.
(a+b, a-b)
Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x ______
Find distance between point Q(3, – 7) and point R(3, 3)
Solution: Suppose Q(x1, y1) and point R(x2, y2)
x1 = 3, y1 = – 7 and x2 = 3, y2 = 3
Using distance formula,
d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `sqrt(square - 100)`
∴ d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `square`
The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
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:
If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by ______.
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 distance of the point P(–6, 8) from the origin is ______.
Find the distance between the points O(0, 0) and P(3, 4).
