Advertisements
Advertisements
प्रश्न
Find the distance between the following pairs of points:
(a, b), (−a, −b)
Find the distance between the following pairs of points:
(-a, -b) and (a, b)
उत्तर
Distance between (a, b) and (−a, −b) is given by
l = `sqrt((a-(-a))^2+(b-(-b))^2)`
= `sqrt((2a)^2 + (2b)^2)`
= `sqrt(4a^2+4b^2)`
= `2sqrt(a^2 + b^2)`
संबंधित प्रश्न
If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that bx = ay.
If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay
Find the distance between the following pairs of points:
(−5, 7), (−1, 3)
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
Find the distance of a point P(x, y) from the origin.
Given a line segment AB joining the points A(–4, 6) and B(8, –3). Find
1) The ratio in which AB is divided by y-axis.
2) Find the coordinates of the point of intersection.
3) The length of AB.
Find the distance between the points
P(a + b,a - b)andQ(a -b,a + b)
Find the distance of the following points from the origin:
(i) A(5,- 12)
Find the distance of the following points from the origin:
(iii) C (-4,-6)
Using the distance formula, show that the given points are collinear:
(1, -1), (5, 2) and (9, 5)
Find x if distance between points L(x, 7) and M(1, 15) is 10.
Find the distances between the following point.
P(–6, –3), Q(–1, 9)
If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance
2AB is equal to
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then ______.
Find the distance of the following point from the origin :
(5 , 12)
Find the distance between the following point :
(sec θ , tan θ) and (- tan θ , sec θ)
Find the distance between the following point :
(Sin θ - cosec θ , cos θ - cot θ) and (cos θ - cosec θ , -sin θ - cot θ)
Find the relation between a and b if the point P(a ,b) is equidistant from A (6,-1) and B (5 , 8).
Find the distance between P and Q if P lies on the y - axis and has an ordinate 5 while Q lies on the x - axis and has an abscissa 12 .
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.
Show that the points (2, 0), (–2, 0), and (0, 2) are the vertices of a triangle. Also, a state with the reason for the type of triangle.
Find the distance between the points (a, b) and (−a, −b).
Find the distance between the origin and the point:
(-5, -12)
A point P (2, -1) is equidistant from the points (a, 7) and (-3, a). Find a.
KM is a straight line of 13 units If K has the coordinate (2, 5) and M has the coordinates (x, – 7) find the possible value of x.
If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x
Show that A(1, 2), (1, 6), C(1 + 2 `sqrt(3)`, 4) are vertices of a equilateral triangle
A circle drawn with origin as the centre passes through `(13/2, 0)`. The point which does not lie in the interior of the circle is ______.
If the distance between the points (4, P) and (1, 0) is 5, then the value of p is ______.
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
Find the points on the x-axis which are at a distance of `2sqrt(5)` from the point (7, – 4). How many such points are there?
What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?
If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.
Find distance between points P(– 5, – 7) and Q(0, 3).
By distance formula,
PQ = `sqrt(square + (y_2 - y_1)^2`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(125)`
= `5sqrt(5)`
|
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.
