Advertisements
Advertisements
प्रश्न
Find the distance between the following pair of points:
(asinα, −bcosα) and (−acos α, bsin α)
Advertisements
उत्तर
The distance d between two points (x1, y1) and (x2, y2) is given by the formula.
`d = sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)`
The two given points are (asinα, −bcosα) and (−acos α, bsin α)
The distance between these two points is
`d = sqrt((a sin alpha + a cos alpha)^2 + (- b cos alpha - bsin alpha)^2)`
`= sqrt(a^2(sin alpha + cos alpha)^2 + b^2(-1)^2(cos alpha + sin alpha))`
`= sqrt(a^2(sin alpha + cos alpha)^2 + b^2(sin alpha + cos alpha))`
`= sqrt((a^2 + b^2)(sin alpha + cos alpha))`
`d = (sin alpha + cos alpha)sqrt(a^2 + b^2)`
Hence the distance is `(sin alpha + cos alpha)sqrt((a^2 + b^2))`
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
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)
The length of a line segment is of 10 units and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.
Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.
Find the distance between the points
(i) A(9,3) and B(15,11)
For what values of k are the points (8, 1), (3, –2k) and (k, –5) collinear ?
Determine whether the point is collinear.
R(0, 3), D(2, 1), S(3, –1)
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 between the following point :
(p+q,p-q) and (p-q, p-q)
Find the distance of a point (7 , 5) from another point on the x - axis whose abscissa is -5.
Find the value of m if the distance between the points (m , -4) and (3 , 2) is 3`sqrt 5` units.
Find the coordinates of the points on the y-axis, which are at a distance of 10 units from the point (-8, 4).
Find the distance of the following points from origin.
(5, 6)
Find the distance of the following points from origin.
(a+b, a-b)
Find the distance of the following points from origin.
(a cos θ, a sin θ).
By using the distance formula prove that each of the following sets of points are the vertices of a right angled triangle.
(i) (6, 2), (3, -1) and (- 2, 4)
(ii) (-2, 2), (8, -2) and (-4, -3).
Find distance between point A(–1, 1) and point B(5, –7):
Solution: Suppose A(x1, y1) and B(x2, y2)
x1 = –1, y1 = 1 and x2 = 5, y2 = – 7
Using distance formula,
d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
∴ d(A, B) = `sqrt(square +[(-7) + square]^2`
∴ d(A, B) = `sqrt(square)`
∴ d(A, B) = `square`
Show that the points (0, –1), (8, 3), (6, 7) and (– 2, 3) are vertices of a rectangle.
The distance of the point (α, β) from the origin is ______.
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.
