Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-3, 5) B(3, 1), C (0, 3), D(-1, -4)
Determine the ratio in which the straight line x - y - 2 = 0 divides the line segment
joining (3, -1) and (8, 9).
If the point C ( - 2,3) is equidistant form the points A (3, -1) and Bx (x ,8) , find the value of x. Also, find the distance between BC
The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, −3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another point D such that ABCD is a rhombus.
Points A(-1, y) and B(5,7) lie on the circle with centre O(2, -3y).Find the value of y.
Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).
ΔXYZ ∼ ΔPYR; In ΔXYZ, ∠Y = 60o, XY = 4.5 cm, YZ = 5.1 cm and XYPY =` 4/7` Construct ΔXYZ and ΔPYR.
What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°)?
Write the condition of collinearity of points (x1, y1), (x2, y2) and (x3, y3).
If the distance between the points (3, 0) and (0, y) is 5 units and y is positive. then what is the value of y?
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
The ratio in which the line segment joining P (x1, y1) and Q (x2, y2) is divided by x-axis is
Find the coordinates of the point of intersection of the graph of the equation x = 2 and y = – 3
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
The points (–5, 2) and (2, –5) lie in the ______.
The points whose abscissa and ordinate have different signs will lie in ______.
(–1, 7) is a point in the II quadrant.
If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).
