Moving point problem of mathematics in grade two of junior high school

Solution: According to the meaning of the question, OA= 1, OC=3, OB=√2.

∴tan∠BAC =√3

∴∠BAC =60

Similarly ∠ ACB = 30

If △ABC is similar to △ABP,

There are four situations.

(1)P is on the extension line of CB, and BP/AB =1√ 3. At this time, the coordinates of point P are (1, 4/3 √ 3).

(2)P is on the extension line of CB, BP/AB=√3, and the coordinate of point P is (3,2 √ 3).

(3)P is on CB, BP/AB =1√ 3, and the coordinate of point P is (-1, 2/3 √ 3).

(4)P is on CB, BP/AB√3, and the coordinate of point P is (-3,0).