Advertisements
Advertisements
प्रश्न
Show that (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.
Advertisements
उत्तर
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
संबंधित प्रश्न
Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.
Find the coordinates of the circumcentre of the triangle whose vertices are (8, 6), (8, – 2) and (2, – 2). Also, find its circum radius
A(–8, 0), B(0, 16) and C(0, 0) are the vertices of a triangle ABC. Point P lies on AB and Q lies on AC such that AP : PB = 3 : 5 and AQ : QC = 3 : 5. Show that : PQ = `3/8` BC.
Find the point on the x-axis equidistant from the points (5,4) and (-2,3).
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT
If the point (x, y) is at equidistant from the point (a + b, b – a) and (a-b, a + b). Prove that ay = bx.
Find distance CD where C(–3a, a), D(a, –2a).
Show that A(1, 2), (1, 6), C(1 + 2`sqrt(3)`, 4) are vertices of an equilateral triangle.
Seg OA is the radius of a circle with centre O. The coordinates of point A is (0, 2) then decide whether the point B(1, 2) is on the circle?
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.
