Question

The base BC of an equilateral triangle ABC lies on y-axis. I the coordinates of the point C ate(0,-3). The origin is the midpoint of the base BC, find the coordinates of the points A and B?

Answer 1

see explanation.

Explanation:

!
Given base `BC` lies on y-axis, `C=(0,-3)`, and origin `O(0,0)` is the midpoint,
`=> OC=3` units,
`=> OB=OC=3` units,
`=>` coordinates of `B=(0,3)`
`=> BC=OB+OC=3+3=6` units
given `DeltaABC` is equilateral,
`=> AO` is perpendicular to `BC and AB=BC=6` units,
`=> DeltaAOB` is a right triangle,
By Pythagorean theorem, we know,
`=> AO^2=AB^2-OB^2`,
`=> AO^2=6^2-3^2=36-9=27`,
`=> AO=sqrt27=sqrt(9xx3)=3sqrt3` units
`=>` coordinates of `A(x,y)=(-3sqrt3,0)`
Similarly, coordinates of `A'(x',y')=(3sqrt3,0)`