2
Question
If (-4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the (i) interior, (ii) exterior of the triangle.
If (-4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the (i) interior, (ii) exterior of the triangle.
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Solution
B(-4,3) C (4,3)
BC = 
= 8
It is an equilateral triangle, so
AB=8
AC=8
AB=
AC =
From (i) and (ii)
16x = 0
x =0
For (0,3+4
), Origin lies outside the triangle
For ( 0, 3 - 4
), Origin lies inside the triangle.
B(-4,3) C (4,3)
BC =
= 8It is an equilateral triangle, so
AB=8
AC=8
AB=
AC =
From (i) and (ii)
16x = 0
x =0
For (0,3+4
), Origin lies outside the triangleFor ( 0, 3 - 4
), Origin lies inside the triangle. Suggest Corrections
42
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