locate the points A (1, 2, )B(3, 4) c(5, 2 ) on a graph sheet taking suitable Axis write the coordinates of the 4.3 in order to complete the Rhombus ABCD measure angles of the Rhombus and check whether they are equal or not
Answers
locate the points A (1, 2), B( 3, 4) and C (5, 2) on a graph sheet taking suitable Axis. write the co-ordinate of the fourth point D in order to complete the Rhombus ABCD. measure the diagonals of the Rhombus and check whether they are equal or not
AB = √((3-1)² + (4-2)²) = √(4 +4) = √8
BC = √((5-3)² + (2-4)²) = √(4 +4) = √8
AC = √((5-1)² + (2-2)²) = √16 = 4
AD = CD = √8 ( as all sides are equal for a rhombus)
Let say D = (x , y)
AD = √((x-1)² + (y-2)²) = √8
CD = √((x-5)² + (y-2)²) = √8
√((x-1)² + (y-2)²) = √((x-5)² + (y-2)²)
squaring both sides
(x-1)² + (y-2)² = (x-5)² + (y-2)²
=> x² + 1 - 2x = x² + 25 - 10x
=> 8x = 24
=> x = 3
Putting x = 3 in AD
√((3-1)² + (y-2)²) = √8
4 + (y-2)² = 8
=> (y-2)² = 4
=> y-2 = ±2
y = 0 or 4
D = (3,0) as (3,4) is point B
Diagonal BD = √((3-3)² + (0-4)²) = √16 = 4
Diagonals AC = BD = 4
so diagonals are equal