Question

ABC is an equilateral triangle of side 3units.Find the coordinates of the vertices B and C if A(2,0) and B lie on x-axis and the vertex C is in the first quadrant

Answer 1

Answer:

B( 5 or -1 , 0) and C (3.5 or 0.5, 2.6)

Step-by-step explanation:

Let the coordinates of  B and C be (z,0) and (x,y ) respectively

According to question AB=BC=AC = 3 units

therefore

$AB= \sqrt{(z-2)^2+(0-0)^2}$

$3= \sqrt{(z-2)^2+(0-0)^2}$

squaring both sides and Solving we get z= 5,-1

Similarly, $AC= \sqrt{(y-2)^2+(x-0)^2}$

$3= \sqrt{(y-0)^2+(x-2)^2}$

squaring both sides we get $9= (y)^2+(x-2)^2$...........1

also,  $BC= \sqrt{(y-0)^2+(x-z)^2}$

putting the value of z we get

$3= \sqrt{(y-0)^2+(x-5)^2}$

squaring we get

$9= (y)^2+(x-5)^2$.........2

solving 1 and 2 we get x= 3.5 and y = 2.6 units

also we take z= -1 then

x= 0.5 and y= 2.6