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
Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.
Find the distance of a point P(x, y) from the origin.
Find the distance between the following pair of points:
(a+b, b+c) and (a-b, c-b)
Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two
vertices.
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.
Find the distance between the following point :
(p+q,p-q) and (p-q, p-q)
Find the relation between a and b if the point P(a ,b) is equidistant from A (6,-1) and B (5 , 8).
From the given number line, find d(A, B):
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.
Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(–1, 1) and B(3, 3).
