Advertisements
Advertisements
प्रश्न
Find the distance between the points O(0, 0) and P(3, 4).
उत्तर
O(0, 0), P(3, 4)
∴ `(x_1, y_1) = (0, 0)`
`(x_2, y_2) = (3, 4)`
∴ `x_1=0, y_1= 0`
`x_2 = 3, y_2 = 4`
d(OP) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt((3 - 0)^2 + (4 - 0)^2`
= `sqrt((3)^2 + (4)^2)`
= `sqrt(9 + 16)`
= `sqrt(25)`
d(OP) = 5 units
APPEARS IN
संबंधित प्रश्न
Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
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.
Find the distance of a point P(x, y) from the origin.
Find the distance of the following points from the origin:
(ii) B(-5,5)
Using the distance formula, show that the given points are collinear:
(-1, -1), (2, 3) and (8, 11)
Determine whether the points are collinear.
A(1, −3), B(2, −5), C(−4, 7)
Find the distance between the following point :
(sin θ , cos θ) and (cos θ , - sin θ)
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.
Prove that the points (0,3) , (4,3) and `(2, 3+2sqrt 3)` are the vertices of an equilateral triangle.
Prove that the points (5 , 3) , (1 , 2), (2 , -2) and (6 ,-1) are the vertices of a square.
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.
Find the distance of the following points from origin.
(5, 6)
If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x
The distance of the point P(–6, 8) from the origin is ______.
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below. |
Based on the above information answer the following questions using the coordinate geometry.
- Find the distance between Lucknow (L) to Bhuj (B).
- If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
- Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P)
[OR]
Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).
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.