Advertisements
Advertisements
प्रश्न
A point P lies on the x-axis and another point Q lies on the y-axis.
If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.
Advertisements
उत्तर
The co-ordinates of P and Q are (-12, 0) and (0, -16) respectively.
PQ = `sqrt((-12 - 0)^2 + (0 + 16)^2)`
= `sqrt(144 + 256)`
= `sqrt(400)`
= 20
APPEARS IN
संबंधित प्रश्न
Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.
Find the distance between the following pair of points:
(asinα, −bcosα) and (−acos α, bsin α)
Using the distance formula, show that the given points are collinear:
(–1, –1), (2, 3) and (8, 11)
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
In what ratio does the point P(−4, y) divides the line segment joining the points A(−6, 10) and B(3, −8)? Hence find the value of y.
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the ordinate of point P.
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`
Show that the point (11, –2) is equidistant from (4, –3) and (6, 3).
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 ______.
Read the following passage:
|
Alia and Shagun are friends living on the same street in Patel Nagar. Shagun's house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point O, i.e., the origin, Alia's house is at A. Shagun's house is at B and library is at C. |
Based on the above information, answer the following questions.

- How far is Alia's house from Shagun's house?
- How far is the library from Shagun's house?
- Show that for Shagun, school is farther compared to Alia's house and library.
OR
Show that Alia’s house, shagun’s house and library for an isosceles right triangle.
