Advertisements
Advertisements
Questions
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)
Advertisements
Solution
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)`
RELATED QUESTIONS
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.
If the point P(x, y ) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.
Given a triangle ABC in which A = (4, −4), B = (0, 5) and C = (5, 10). A point P lies on BC such that BP : PC = 3 : 2. Find the length of line segment AP.
Find the distance between the points
A(1,-3) and B(4,-6)
Find the distance of the following points from the origin:
(i) A(5,- 12)
Using the distance formula, show that the given points are collinear:
(6, 9), (0, 1) and (-6, -7)
Find the value of m if the distance between the points (m , -4) and (3 , 2) is 3`sqrt 5` units.
x (1,2),Y (3, -4) and z (5,-6) are the vertices of a triangle . Find the circumcentre and the circumradius of the triangle.
Prove that the points (1 ,1),(-4 , 4) and (4 , 6) are the certices of an isosceles triangle.
Prove that the points (5 , 3) , (1 , 2), (2 , -2) and (6 ,-1) are the vertices of a square.
Prove that the points (0 , 2) , (1 , 1) , (4 , 4) and (3 , 5) are the vertices of a rectangle.
ABCD is a square . If the coordinates of A and C are (5 , 4) and (-1 , 6) ; find the coordinates of B and D.
In what ratio does the point P(−4, y) divides the line segment joining the points A(−6, 10) and B(3, −8)? Hence find the value of y.
Find the coordinates of the points on the y-axis, which are at a distance of 10 units from the point (-8, 4).
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the ordinate of point P.
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
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.

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.
(5, 6)
Show that the quadrilateral with vertices (3, 2), (0, 5), (- 3, 2) and (0, -1) is a square.
Find distance between points O(0, 0) and B(–5, 12).
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`
Find distance CD where C(–3a, a), D(a, –2a).
Show that the point (0, 9) is equidistant from the points (–4, 1) and (4, 1).
Show that A(1, 2), (1, 6), C(1 + 2`sqrt(3)`, 4) are vertices of an equilateral triangle.
The distance between the points A(0, 6) and B(0, -2) is ______.
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.
