As shown in the figure, in the plane rectangular coordinate system, the length of ABC side of equilateral triangle is 3 / 2, and BC side is on the negative half axis of X, e (0, a), f (B, 0) If the equilateral triangle ABC starts from the origin O and moves to the left, when B and f coincide, AC intersects EF at N and the length of CN is calculated (2) In ABC motion of equilateral triangle, AB intersects EF with M. when the area of triangle AOM is √ (3) / 2, m coordinate is obtained

As shown in the figure, in the plane rectangular coordinate system, the length of ABC side of equilateral triangle is 3 / 2, and BC side is on the negative half axis of X, e (0, a), f (B, 0) If the equilateral triangle ABC starts from the origin O and moves to the left, when B and f coincide, AC intersects EF at N and the length of CN is calculated (2) In ABC motion of equilateral triangle, AB intersects EF with M. when the area of triangle AOM is √ (3) / 2, m coordinate is obtained

1. Calculate the EF line according to the E.F point, and then calculate the AC line according to the A.C point
Then CN = Y / sin60
2. Let m coordinate x.y, B coordinate Z, 0
The first equation is EF line, the second equation is ab line, and the third equation is AOM area = ABO area BMO area
I can only tell you the algorithm. I think it's too complicated to calculate. The main reason is that AB is not a specific value

For an equilateral triangle ABC whose side length is 8, establish an appropriate rectangular coordinate system and write out the coordinates of each point

Take the bottom edge as the x-axis and the height of this edge as the y-axis,
Then the coordinates of the three vertices are
（-4,0）（4,0）（0,4√3）

As shown in the figure, for the positive △ ABC with side length 6, establish an appropriate rectangular coordinate system and write out the coordinates of each vertex

As shown in the figure, take the straight line where BC is as the x-axis and the straight line passing through a perpendicular to BC as the y-axis to establish the coordinate system, O as the origin, ∵△ ABC is positive △ ABC, O as the midpoint of BC, and the side length of △ ABC is 6, ∵ Bo = co = 3. In RT △ AOB, AB2 = AO2 + Bo2, ∵ Ao = 33, ∵ B (- 3,0), C (3,0), a (0,33)

As shown in the figure, for the positive △ ABC with side length 6, establish an appropriate rectangular coordinate system and write out the coordinates of each vertex

As shown in the figure, take the straight line where BC is as the x-axis and the straight line passing through a perpendicular to BC as the y-axis to establish the coordinate system, O as the origin, ∵△ ABC is positive △ ABC, O as the midpoint of BC, and the side length of △ ABC is 6, ∵ Bo = co = 3. In RT △ AOB, AB2 = AO2 + Bo2, ∵ Ao = 33, ∵ B (- 3,0), C (3,0), a (0,33)