Advertisements
Advertisements
Question
Show that (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.
Advertisements
Solution
Let the given points be A (-3, 2), B (-5, -5), C (2, -3) and D (4, 4).
AB = `sqrt((-5 + 3)^2 + (-5 - 2)^2) = sqrt(4+49) = sqrt(53)`
BC = = `sqrt((2+5)^2 + (-3+5)^2) = sqrt(49+4) = sqrt(53)`
CD= = `sqrt((4 - 2)^2 + (4+3)^2) = sqrt(4 + 49) = sqrt(53)`
DA = `sqrt((-3 - 4)^2 + (2 - 4)^2) = sqrt(49+4) = sqrt(53)`
AC =`sqrt((2+3)^2 + (-3 - 2)^2) = sqrt(25+25) = 5sqrt(2)`
BD =`sqrt((4+5)^2 + (4+5)^2) = sqrt(81+ 81) = 9sqrt(2)`
Since, AB = BC = CD = DA and AC ≠ BD
The given vertices are the vertices of a rhombus.
APPEARS IN
RELATED QUESTIONS
Find the distance between the following pairs of points:
(a, b), (−a, −b)
Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
AB and AC are the two chords of a circle whose radius is r. If p and q are
the distance of chord AB and CD, from the centre respectively and if
AB = 2AC then proove that 4q2 = p2 + 3r2.
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
Find the distance between the following pairs of point in the coordinate plane :
(13 , 7) and (4 , -5)
The distance between the points (0, 5) and (–5, 0) is ______.
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
If the distance between the points (4, P) and (1, 0) is 5, then the value of p is ______.
|
Case Study Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. |
- Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
- After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?
The distance between the points (0, 5) and (–3, 1) is ______.
