Advertisements
Advertisements
प्रश्न
Find the distance between the following pairs of points:
(2, 3), (4, 1)
Find the distance between the following pairs of points:
A (2, 3), B (4, 1)
Advertisements
उत्तर १
l = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
= `sqrt((4 - 2)^2 + (1 - 3)^2)`
= `sqrt(2^2 + (- 2)^2)`
= `sqrt(4 + 4)`
= `sqrt(8)`
= `sqrt(4 × 2)`
= `2sqrt(2)` units
उत्तर २
A (2, 3), B (4, 1)
Suppose the coordinates of point A are (x1, y1) and those of point B are (x2, y2).
x1 = 2, y1 = 3, x2 = 4, y2 = 1
According to distance formula,
d(A,B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
d(A,B) = `sqrt((4 - 2)^2 + (1 - 3)^2)`
d(A,B) = `sqrt(2^2 + (- 2)^2)`
d(A,B) = `sqrt(4 + 4)`
d(A,B) = `sqrt(8)`
d(A,B) = `sqrt(4 × 2)`
d(A,B) = `2sqrt(2)`
The distance between points A and B is `2sqrt(2)` units.
संबंधित प्रश्न
If the opposite vertices of a square are (1, – 1) and (3, 4), find the coordinates of the remaining angular points.
Find the distance of a point P(x, y) from the origin.
ABC is a triangle and G(4, 3) is the centroid of the triangle. If A = (1, 3), B = (4, b) and C = (a, 1), find ‘a’ and ‘b’. Find the length of side BC.
Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two
vertices.
Show that the points A(1, 2), B(1, 6), C(1 + 2`sqrt3`, 4) are vertices of an equilateral triangle.
Find the distances between the following point.
A(a, 0), B(0, a)
Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle.
Find the distance between the following point :
(sin θ , cos θ) and (cos θ , - sin θ)
Find the value of a if the distance between the points (5 , a) and (1 , 5) is 5 units .
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 (a, b), (a + 3, b + 4), (a − 1, b + 7) and (a − 4, b + 3) are the vertices of a parallelogram.
Find the distance between the points (a, b) and (−a, −b).
Find the point on y-axis whose distances from the points A (6, 7) and B (4, -3) are in the ratio 1: 2.
Find the distance of the following points from origin.
(a+b, a-b)
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`
Seg OA is the radius of a circle with centre O. The coordinates of point A is (0, 2) then decide whether the point B(1, 2) is on the circle?
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?
If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.
The distance between the points (0, 5) and (–3, 1) is ______.
