# two vertices of a triangle are (1,2), (3,5), and the centeroid is at the origin. Find the third vertex. Find the coordinates (x,y) of a point whose distance from points (3,5) is 5 units & that from (0,1) is 10 units , given that 3x=2y If 3b is the length of a side of an equilateral triangle ABC ,base BC lies on x-axis & B lies of origin , find the coordinate of vertices of ABC

(a) let the vertices of the triangle be A(1,2), B(3,5) and .

therefore centroid of the triangle ABC is given by:

given: the centroid is the origin i.e. (0,0).

therefore

hence the coordinates of third vertex is (-4,-7).

(2)nd question:

distance of (x,y) from the point (3,5) is 5 units.

and distance of (x,y) from the point (0,1) is 10 units.

subtracting equation (1) from (2):

since 3x=2y put this in (3)

hence the desired point is (6,9).

3rd question

the coordinates of B is (0,0).

since BC lies on x-axis. and length of the side is 3b.

since C is on x-axis and at a distance of 3b units.

the coordinates of C will be either (3b,0) or (-3b,0)

now draw perpendicular from A to BC, let it intersect BC at D.

D will be the mid-point of BC, BD=3b/2

therefore

the coordinates of A (when coordinates of C is (3b,0)) is

the coordinates of A (when coordinates of C is (-3b,0)) is

• 19

x =-4 ,y = -7

• 4

x=-4, y=-7

• 8
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