(1, ) and (1, -
)
Step-by-step explanation:
Step 1 :
The co ordinates of the given equilateral triangle are A(-2,1) and B(4,1)
The distance between these 2 points is the length of the given triangle
Distance between the 2 points is = sqrt (sq(4-(-2)) + sq(1-1)) = 6
Hence the given triangle has 3 equal side of length 6 unit.
Step 2:
The length of the other side should be 6. Let (x,y) be the co-ordinate of the point C
We have then x = 1 (because the perpendicular from C to AB bisects AB we have the point C to have the x co-ordinate as 1)
Also we have the distance between the point B(4,1) and C(1,y) to be 6 as this is an equilateral triangle
Hence = 6
=> 9 + 1 + -2 y = 6
=> -2 y - 26 = 0
=> y = 2± sqrt(4+104) / 2 = 1 ± sqrt(27)
Hence the possible co ordinates of C are (1, ) and (1, -
)