The coordinates of three vertices of a rhombus are given in the diagram.

a. Deduce the coordinates of the missing vertex D.
The coordinates of D are (6, 6).

b. Justify your answer using the properties of the rhombus.
The diagonals of a rhombus intersect at right angles. Vertices A and C lie in the same vertical line, because their x-coordinates are the same. Therefore, D must be on the same horizontal line as B. A rhombus also has two lines of symmetry, therefore D must have coordinates (6, 6) as shown.

Transcribed Image Text:

B(2, 6) C(4,9) A(4,3)