Advertisements
Advertisements
प्रश्न
Find distance between point A(–3, 4) and origin O.
पर्याय
7 cm
10 cm
5 cm
–5cm
Advertisements
उत्तर
5 cm
Explanation:
Let A(x1, y1) = A(–3, 4) and O(x2, y2) = O(0, 0)
Here, x1 = –3, y1 = 4, x2 = 0, y2 = 0
By distance formula,
d(A, O) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
= `sqrt([0 - (-3)]^2 + (0- 4)^2)`
= `sqrt(9 + 16)`
= `sqrt(25)`
= 5 cm
APPEARS IN
संबंधित प्रश्न
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.
Find the distance of the following points from the origin:
C(–4, –6)
If the point A(x, 2) is equidistant from the points B(8, –2) and C(2, –2), find the value of x. Also, find the length of AB.
Using the distance formula, show that the given points are collinear:
(–2, 5), (0, 1) and (2, –3)
Determine whether the points are collinear.
P(–2, 3), Q(1, 2), R(4, 1)
Show that the points A(1, 2), B(1, 6), C(1 + 2`sqrt3`, 4) are vertices of an equilateral triangle.
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 :
(6 , 8)
P and Q are two points lying on the x - axis and the y-axis respectively . Find the coordinates of P and Q if the difference between the abscissa of P and the ordinates of Q is 1 and PQ is 5 units.
Prove that the points (0 , 0) , (3 , 2) , (7 , 7) and (4 , 5) are the vertices of a parallelogram.
ABCD is a square . If the coordinates of A and C are (5 , 4) and (-1 , 6) ; find the coordinates of B and D.
Find the distance between the origin and the point:
(8, −15)
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
Show that the quadrilateral with vertices (3, 2), (0, 5), (- 3, 2) and (0, -1) is a square.
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x = ______.
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
Show that Alia's house, Shagun's house and library for an isosceles right triangle.
|
Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players is represented as points on a coordinate plane. |
- At an instance, the midfielders and forward formed a parallelogram. Find the position of the central midfielder (D) if the position of other players who formed the parallelogram are :- A(1, 2), B(4, 3) and C(6, 6)
- Check if the Goal keeper G(–3, 5), Sweeper H(3, 1) and Wing-back K(0, 3) fall on a same straight line.
[or]
Check if the Full-back J(5, –3) and centre-back I(–4, 6) are equidistant from forward C(0, 1) and if C is the mid-point of IJ. - If Defensive midfielder A(1, 4), Attacking midfielder B(2, –3) and Striker E(a, b) lie on the same straight line and B is equidistant from A and E, find the position of E.
