Q8 of 49 Page 167

Show that the points (-4, -7), (-1, 2), (8, 5) and (5, -4) taken in order are the vertices of a rhombus.

(Hint: Area of rhombus product of its diagonals)

Let the points be

A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4)


Length of diagonals


AC =


AC =


AC =


BD =


BD =


BD =


⇒ Area of Rhombus = 1/2 × Product of diagonals


= =


= 72 units


⇒ Area of triangles


Area ΔABD =


=


=


=


= 36


⇒ Are


a ΔBCD =


=


=


=


= 36


Sum of area of triangles = 36 + 36 = 72 units


Thus proved


More from this chapter

All 49 →
6

Show that the following points form an equilateral triangle A(a, 0), B(-a, 0),

7

Prove that the point (-7, -3), (5, 10), (15, 8) and (3,-5) taken in order are the corners of a parallelogram. And find its area.

 9

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.

(-1, -2), (1, 0), (-1, 2), (-3, 0)

 9

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.

(-3, 5), (3, 1), (1, -3), (-1,-4)