ABC is an equilateral triangle as shown in the figure. Find the coordinates of its vertices.
Y
B
с
x't
0
6
Answers
Correct question :
ABC is an equilateral triangle as shown in the figure. Find the coordinates of its vertices.
Solution :
From figure,
BC = 4 units.
As ABC is an equilateral triangle,
AB = AC =4 units.
From A, draw AM ⊥ BC, then M is mid-point of BC.
So,
BM = ½ BC = ½ x4 units = 2 units.
In ΔABM, ∠M = 90°. By Pythagoras theorem, we get
AB²= AM² + BM²
4² = AM² +2²
AM² = 16 - 4
AM² = 12
AM = 2√3 units.
From figure,
OM = OB + BM
= (1 +2) units
= 3 units.
Clearly, coordinates of B and C are (1, 0) and (5, 0) respectively.
As OM = 3 units and AM of A = 2√3 units, therefore, coordinates are (3,2√3).
(3,2√3)
Step-by-step explanation:
Correct question :
ABC is an equilateral triangle as shown in the figure. Find the coordinates of its vertices.
Solution :
From figure,
BC = 4 units.
As ABC is an equilateral triangle,
AB = AC =4 units.
From A, draw AM ⊥ BC, then M is mid-point of BC.
So,
BM = ½ BC = ½ x4 units = 2 units.
In ΔABM, ∠M = 90°. By Pythagoras theorem, we get
AB²= AM² + BM²
4² = AM² +2²
AM² = 16 - 4
AM² = 12
AM = 2√3 units.
From figure,
OM = OB + BM
= (1 +2) units
= 3 units.
Clearly, coordinates of B and C are (1, 0) and (5, 0) respectively.
As OM = 3 units and AM of A = 2√3 units, therefore, coordinates are (3,2√3).