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प्रश्न
What is the distance of the point (– 5, 4) from the origin?
विकल्प
3 units
`sqrt(14)` units
`sqrt(31)` units
`sqrt(41)` units
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उत्तर
`sqrt(41)` units
Explanation:
Given points are (– 5, 4) and (0, 0).
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
Here, x1 = – 5, y1 = 4, x2 = 0, y2 = 0
∴ Distance = `sqrt((0 - (- 5))^2 + (0 - 4)^2`
= `sqrt(5^2 + 4^2)`
= `sqrt(25 + 16)`
= `sqrt(41)`
Thus, the distance is `sqrt(41)` units.
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संबंधित प्रश्न
Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
Find the values of x for which the distance between the points P(x, 4) and Q(9, 10) is 10 units.
Using the distance formula, show that the given points are collinear:
(–1, –1), (2, 3) and (8, 11)
Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle.
Find the point on the x-axis equidistant from the points (5,4) and (-2,3).
Find the coordinate of O , the centre of a circle passing through P (3 , 0), Q (2 , `sqrt 5`) and R (`-2 sqrt 2` , -1). Also find its radius.
Find the coordinates of O, the centre passing through A( -2, -3), B(-1, 0) and C(7, 6). Also, find its radius.
Prove that the points (7 , 10) , (-2 , 5) and (3 , -4) are vertices of an isosceles right angled triangle.
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
PQR is an isosceles triangle . If two of its vertices are P (2 , 0) and Q (2 , 5) , find the coordinates of R if the length of each of the two equal sides is 3.
Prove that the points A (1, -3), B (-3, 0) and C (4, 1) are the vertices of an isosceles right-angled triangle. Find the area of the triangle.
Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).
Find distance between point A(–3, 4) and origin O.
The distance between the points A(0, 6) and B(0, –2) is ______.
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, –9) and has diameter `10sqrt(2)` units.
Find the distance between the points O(0, 0) and P(3, 4).
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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.
