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
Answers
Answer:
D = (3,0)
diagonals are equal
Step-by-step explanation:
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
Answer:
it's diagonals are equal each measuring 4 CM it might help you
