Advertisements
Advertisements
Question
Find the distance between the following pair of points:
(a, 0) and (0, b)
Solution
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 (a, 0) and (0, b)
The distance between these two points is
`d = sqrt((a - 0)^2 + (0 - b)^2)`
`= sqrt((a)^2 + (-b)^2)`
`d = sqrt(a^2 + b^2)`
Hence the distance is `sqrt(a^2 + b^2)`
APPEARS IN
RELATED QUESTIONS
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
If the point C ( - 2,3) is equidistant form the points A (3, -1) and Bx (x ,8) , find the value of x. Also, find the distance between BC
If the point ( x,y ) is equidistant form the points ( a+b,b-a ) and (a-b ,a+b ) , prove that bx = ay
Show that the following points are the vertices of a square:
(i) A (3,2), B(0,5), C(-3,2) and D(0,-1)
Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.
Show that the points A(2,1), B(5,2), C(6,4) and D(3,3) are the angular points of a parallelogram. Is this figure a rectangle?
Find the coordinates of the midpoints of the line segment joining
P(-11,-8) and Q(8,-2)
If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value of k.
Show that the points (−2, 3), (8, 3) and (6, 7) are the vertices of a right triangle ?
The distance of the point P (4, 3) from the origin is
If (0, −3) and (0, 3) are the two vertices of an equilateral triangle, find the coordinates of its third vertex.
Find the value of k if points A(k, 3), B(6, −2) and C(−3, 4) are collinear.
What is the distance between the points \[A\left( \sin\theta - \cos\theta, 0 \right)\] and \[B\left( 0, \sin\theta + \cos\theta \right)\] ?
If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =
The perimeter of the triangle formed by the points (0, 0), (0, 1) and (0, 1) is
The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b)
In which quadrant does the point (-4, -3) lie?
Signs of the abscissa and ordinate of a point in the second quadrant are respectively.
If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has ______.
Abscissa of a point is positive in ______.
