4. In the adjoining figure, ABC is an equilateral triangle. The
coordinates of vertices B and Care (3,0) and (-3,0) respectively.
Find the coordinates of its vertex A.
Answers
Answer:
Given coordinates of B and C are (3, 0) and (-3, 0)
and CD = DB = 3 units
Hence D coincides with the origin.
Since ABC is an equilateral triangle, AB = BC = CA = 6 units
In right triangle ADB, [By Pythagoras theorem]
units
Hence the coordinates of A are
Step-by-step explanation:
AnSwEr
Since ABC is an equilateral triangle, therefore
AB = AC = BC
OB = 3 units ( along + ve direction of x-axis)
OC = -3 units ( Along - ve direction of x-axis)
But side CB = OB - OC
=> CB = 3 - ( -3)
=> CB = 6 units
=> BC = 6 units
=> AC = BC = 6 units
In right traingle AOC, we have
ac {}^{2} = ao^{2} + oc {}^{2}ac
2
=ao
2
+oc
2
(6) {}^{2} = oa {}^{2} + (3) {}^{2}(6)
2
=oa
2
+(3)
2
36 = oa {}^{2} + 936=oa
2
+9
OA {}^{2} = 36 - 9OA
2
=36−9
OA {}^{2} = 27OA
2
=27
OA = 3 \sqrt{3} \: unitsOA=3
3
units
The point A is at
3 \sqrt{3}3
3
and x co-ordinates of A is O
Hence,
The co-ordinates of vertex A are (0, 3✓3)