Advertisements
Advertisements
प्रश्न
Find the distance between the following pair of points:
`(sqrt(3)+1,1)` and `(0, sqrt(3))`
Advertisements
उत्तर
Step 1: Formula
The distance between two points (x1, y1) and (x2, y2) is given by:
`d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
Step 2: Substitute values
`x_1 = sqrt3 + 1, y_1 = 1, x_2 = 0, y_2 = sqrt3`
`d = sqrt((0 - (sqrt3 + 1))^2 + (sqrt3 - 1)^2)`
Step 3: Simplify
`d = sqrt((sqrt3 + 1)^2 + (sqrt3 - 1)^2)`
`= sqrt((3 + 2sqrt3 + 1) + (3 - 2sqrt3 + 1))`
`= sqrt((4 + 2sqrt3) + (4 - 2sqrt3))`
`= sqrt8`
Step 4: Simplify further
`d = 2sqrt2`
APPEARS IN
संबंधित प्रश्न
Find the coordinates of the circumcentre of the triangle whose vertices are (8, 6), (8, – 2) and (2, – 2). Also, find its circum radius
Find value 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)
Find the distance between the following pair of points.
R(0, -3), S(0, `5/2`)
Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.
Prove that the following set of point is collinear :
(4, -5),(1 , 1),(-2 , 7)
Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.
Point P (2, -7) is the centre of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of AB.
Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.
