Advertisements
Advertisements
प्रश्न
Find all possible values of y for which distance between the points is 10 units.
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the distance between the following pairs of points:
(−5, 7), (−1, 3)
Find the distance between the following pairs of points:
(a, b), (−a, −b)
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
Given a triangle ABC in which A = (4, −4), B = (0, 5) and C = (5, 10). A point P lies on BC such that BP : PC = 3 : 2. Find the length of line segment AP.
Find the distance between the points
(i) A(9,3) and B(15,11)
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
Find the distance between the following pairs of point in the coordinate plane :
(13 , 7) and (4 , -5)
Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.
Prove that the points (1 , 1) , (-1 , -1) and (`- sqrt 3 , sqrt 3`) are the vertices of an equilateral triangle.
A point A is at a distance of `sqrt(10)` unit from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice its abscissa.
Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square ABCD.
Show that the quadrilateral with vertices (3, 2), (0, 5), (- 3, 2) and (0, -1) is a square.
Find distance between point A(– 3, 4) and origin O
Show that the points (0, –1), (8, 3), (6, 7) and (– 2, 3) are vertices of a rectangle.
If the distance between the points (4, P) and (1, 0) is 5, then the value of p 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 point on x axis equidistant from I and E is ______.
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.
Find the points on the x-axis which are at a distance of `2sqrt(5)` from the point (7, – 4). How many such points are there?
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.
The distance between the points (0, 5) and (–3, 1) is ______.
