Question

19. (i) If (0,0) and (3, 0) are two vertices of an equilateral triangle, find the third vertex.
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Answer 1

Answer:

Let the the third vertex be (x,y). Side of the equilateral triangle, using distance formula = (32+32) = 32.

Area of equilateral triangle = 3(side)2/4 = 93/2 sq unit.

Area of triangle = (1/2)(3y - 3x)

= 93/2 (3y - 3x)

= 93 y - x = 33       ..............(1)

Using distance formula, since the third vertex must be equidistant from other two,

((x - 3)2 + (y - 3)2)= (x2 + y2)       ((x - 3)2 + (y - 3)2) = (x2 + y2)      

x2 - 6x + 9 + y2 - 6y + 9 = x2 + y2    - 6x + 9 - 6y + 9 = 0 x + y = -3 .............(2)

Solving (1) and (2), x = -3(3+1)/2, y =  3(3-1)/2

Hope this helps . mark as brainlest .

Answer 2

Answer:

answer = the third vertex of the equilateral triangle = (0,2■3) or (3,-■3)