Advertisements
Advertisements
प्रश्न
Prove that the points (0 , 2) , (1 , 1) , (4 , 4) and (3 , 5) are the vertices of a rectangle.
उत्तर
AB = `sqrt ((0 - 1)^2 + (2 - 1)^2) = sqrt 2` units
BC = `sqrt ((1 - 4)^2 + (1 - 4)^2) = 3 sqrt 2` units
CD = `sqrt ((4 - 3)^2 + (4 - 5)^2) = sqrt 2` units
DA = `sqrt ((3 - 0)^2 + (5 - 2)^2) = 3 sqrt 2` units
AC = `sqrt ((4 - 0)^2 + (4 - 2)^2) = sqrt 20 = 2 sqrt 5` units
BC = `sqrt ((3 - 1)^2 + (5 - 1)^2) = sqrt 20 = 2 sqrt 5` units
∵ AB = CD and BC = DA
Also , AC = BD
∴ ABCD is a rectangle.
APPEARS IN
संबंधित प्रश्न
Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.
Find the circumcenter of the triangle whose vertices are (-2, -3), (-1, 0), (7, -6).
Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3)
Using the distance formula, show that the given points are collinear:
(6, 9), (0, 1) and (-6, -7)
For what values of k are the points (8, 1), (3, –2k) and (k, –5) collinear ?
Find x if distance between points L(x, 7) and M(1, 15) is 10.
Show that the points A(1, 2), B(1, 6), C(1 + 2`sqrt3`, 4) are vertices of an equilateral triangle.
Find the distance between the following pairs of point in the coordinate plane :
(7 , -7) and (2 , 5)
Find the distance between the following pairs of point in the coordinate plane :
(13 , 7) and (4 , -5)
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
