Question

The base of the equilateral triangle has an equation of x+2y=3 and one of the vertex is (1,1).find the equation of other two sides

Answer 1

Answer:

Let ABC be the given equilateral triangle with side 2a.

Accordingly, AB = BC = CA = 2a = Assume that base BC lies along the y axis such that the mid-point of BC is

at the origin.

j.e., Oa, where O is the

origin.

Now, it is clear that the coordinates of point Care (0, a), while the

coordinates of point B are (0, -a). It is known that the line joining a vertex of an equilateral triangle wi f the mid-point of its opposite side perpendicular.

Hence, vertex A lies on the y-axis.

On applying Pythagoras theorem to

AOC, we obtain (AC)2 = (OA)2 + (OC)2

- (2a)2 = (OA)2 + a2

4a2 -a2 = (OA)?

(A)2 = 3a2 =

OA = 3a =

:Coordinates of point A = (=30,0) Thus, the vertices of the given On applying Pythagoras theorem to

AOC, we obtain (AC)2 = (OA)2 + (OC)2

=

(2a)2 = (A)2 + a2

4a2 -a2 = (OA)2

(A)2 = 3a2 =

- OA = 3a

:Coordinates of point A = (+V3a,0)

Thus, the vertices of the given

equilateral triangle are (0, a), (0, -a), (V3a, 0) and or (0, a), (0, -a), and

(-13a, 0).

Hope it was helpfull