Advertisements
Advertisements
प्रश्न
Verify that the following points taken in order to form the vertices of a rhombus
A(1, 1), B(2, 1), C(2, 2) and D(1, 2)
Advertisements
उत्तर
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((2 - 1)^2 + (1 - 1)^2`
= `sqrt((1)^2 + (0)^2`
= `sqrt(1)`
= 1
BC = `sqrt((2 - 2)^2 + (2 - 1)^2`
= `sqrt((0)^2 + (1)^2`
= `sqrt(1)`
= 1
CD = `sqrt((1 - 2)^2 + (2 - 2)^2`
= `sqrt((- 1)^2 + (0)^2`
= `sqrt(1)`
= 1
AD = `sqrt((1 - 1)^2 + (2 - 1)^2`
= `sqrt((0)^2 + (1)^2`
= `sqrt(1)`
= 1
AB = BC = CD = AD = 1.
All the four sides are equal.
∴ ABCD is a rhombus.
APPEARS IN
संबंधित प्रश्न
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = 4, y = - 8
On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.
d(P, Q) - d(P, R) = d(Q, R)
Co-ordinates of the pair of a point is given below. Hence find the distance between the pair.
3, 6
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
-9, -1
Find the distance between the following pair of points
(1, 2) and (4, 3)
Find the distance between the following pair of points
(3, −9) and (−2, 3)
Show that the following points taken in order to form an isosceles triangle
A(5, 4), B(2, 0), C(−2, 3)
Show that the following points taken in order to form an isosceles triangle
A(6, −4), B(−2, −4), C(2, 10)
The point (x, y) is equidistant from the points (3, 4) and (−5, 6). Find a relation between x and y
Let A(2, 3) and B(2, −4) be two points. If P lies on the x-axis, such that AP = `3/7` AB, find the coordinates of P.
