Advertisements
Advertisements
प्रश्न
The points A(2, 0), B(9, 1) C(11, 6) and D(4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.
Advertisements
उत्तर
Let A (2, 0); B (9, 1); C (11, 6) and D `(4, 4) be the vertices of a quadrilateral. We have to check if the quadrilateral ABCD is a rhombus or not.
So we should find the lengths of sides of quadrilateral ABCD.
`AB = sqrt((9-2)^2 + (1 - 0)^2)`
`= sqrt(49 + 1)`
`= sqrt50`
`BC= sqrt((11 - 9)^2 + (6 -1)^2)``
`= sqrt(4 + 25)`
`= sqrt29`
`CD = sqrt((11 - 4)^2 + (6 - 4)^2)`
`= sqrt(49 + 4)`
`= sqrt53`
`AD = sqrt((4- 5)^2 + (4 - 0)^2)`
`= sqrt(4 + 16)`
`= sqrty(20)`
All the sides of quadrilateral are unequal. Hence ABCD is not a rhombus.
APPEARS IN
संबंधित प्रश्न
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
On which axis do the following points lie?
R(−4,0)
On which axis do the following points lie?
S(0,5)
Prove that the points (−2, 5), (0, 1) and (2, −3) are collinear.
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
If the poin A(0,2) is equidistant form the points B (3, p) and C (p ,5) find the value of p. Also, find the length of AB.
Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.
Find the co-ordinates of the point which divides the join of A(-5, 11) and B(4,-7) in the ratio 7 : 2
In what ratio does the line x - y - 2 = 0 divide the line segment joining the points A (3, 1) and B (8, 9)?
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
If the vertices of ΔABC be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p
Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles.
Find the value(s) of k for which the points (3k − 1, k − 2), (k, k − 7) and (k − 1, −k − 2) are collinear.
\[A\left( 6, 1 \right) , B(8, 2) \text{ and } C(9, 4)\] are three vertices of a parallelogram ABCD . If E is the mid-point of DC , find the area of \[∆\] ADE.
If \[D\left( - \frac{1}{5}, \frac{5}{2} \right), E(7, 3) \text{ and } F\left( \frac{7}{2}, \frac{7}{2} \right)\] are the mid-points of sides of \[∆ ABC\] , find the area of \[∆ ABC\] .
If P (2, 6) is the mid-point of the line segment joining A(6, 5) and B(4, y), find y.
The distance between the points (cos θ, 0) and (sin θ − cos θ) is
In Fig. 14.46, the area of ΔABC (in square units) is
Abscissa of all the points on the x-axis is ______.
Statement A (Assertion): If the coordinates of the mid-points of the sides AB and AC of ∆ABC are D(3, 5) and E(–3, –3) respectively, then BC = 20 units.
Statement R (Reason): The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.
