Advertisements
Advertisements
प्रश्न
Find distance between points O(0, 0) and B(– 5, 12)
Advertisements
उत्तर
Let O(x1, y1) = O(0, 0) and B(x2, y2) = B(– 5, 12)
∴ x1 = 0, y1 = 0, x2 = – 5, y2 = 12
By distance formula,
d(O, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt((-5 - 0)^2 + (12 - 0)^2`
= `sqrt((-5)^2 + 12^2`
= `sqrt(25 + 144)`
= `sqrt(169)`
∴ d(O, B) = 13 units
∴ The distance between the points O and B is 13 units.
APPEARS IN
संबंधित प्रश्न
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 pair of points:
(asinα, −bcosα) and (−acos α, bsin α)
Find the value of a when the distance between the points (3, a) and (4, 1) is `sqrt10`
Find the distance between the points
A(1,-3) and B(4,-6)
For what values of k are the points (8, 1), (3, –2k) and (k, –5) collinear ?
AB and AC are the two chords of a circle whose radius is r. If p and q are
the distance of chord AB and CD, from the centre respectively and if
AB = 2AC then proove that 4q2 = p2 + 3r2.
Find the distance of the following point from the origin :
(5 , 12)
Find the coordinates of O, the centre passing through A( -2, -3), B(-1, 0) and C(7, 6). Also, find its radius.
The centre of a circle passing through P(8, 5) is (x+l , x-4). Find the coordinates of the centre if the diameter of the circle is 20 units.
Find the distance between the following pairs of points:
(–3, 6) and (2, –6)
Find the co-ordinates of points on the x-axis which are at a distance of 17 units from the point (11, -8).
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the ordinate of point P.
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
Calculate the distance between A (7, 3) and B on the x-axis, whose abscissa is 11.
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
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 ______.
Show that Alia's house, Shagun's house and library for an isosceles right triangle.
Read the following passage:
|
Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle: One such campaign board made by class X student of the school is shown in the figure.
|
Based on the above information, answer the following questions:
- Find the coordinates of the point of intersection of diagonals AC and BD.
- Find the length of the diagonal AC.
-
- Find the area of the campaign Board ABCD.
OR - Find the ratio of the length of side AB to the length of the diagonal AC.
- Find the area of the campaign Board ABCD.
