As shown in the figure, in the plane rectangular coordinate system, the side ab of triangle ABC is on the x-axis, a (- 2,0), C (2,4), s triangle = 6, find the coordinates of point B

As shown in the figure, in the plane rectangular coordinate system, the side ab of triangle ABC is on the x-axis, a (- 2,0), C (2,4), s triangle = 6, find the coordinates of point B

Let B (x, y)
The ordinate of ∵ C is 4 and ab is on the x-axis
The height of Δ ABC is 4
The base of △ ABC = abscissa of AB = | a - abscissa of B = | - 2-x|
And ∵ s △ ABC = 6
The height (ordinate of C) on the side of ｛ 1 ／ 2 &; ab &; ab = 6
I.e. 1 ／ 2 × | - 2-x | × 4 = 6
Ψ x = 1 or - 5
B (1,0) or (- 5,0)

Given a (0,2), B (6,4), if we find a point C on the x-axis and let △ ABC be an isosceles triangle, then the coordinate of C is____ .

Let C (x, 0)
AB^2=6^2+2^2=40
AC^2=x^2+2^2=x^2+4
BC^2=(6-x)^2+4^2=x^2-12x+52
AB = AC, x = 6 (- 6 discard)
AB = BC get x ^ 2-12x + 12 = 0, x = 6 + 3 radical 3, x = 6-3 radical 3
AC = BC is 12x = 48 x = 4

It is known that a (0,0) B (2,1) finds a point C on the x-axis so that the triangle ABC is an isosceles triangle

The idea of solving the problem is to connect AB to do a point on the x-axis of the intersection of the central and vertical lines of AB, which is the required point
AB midpoint (1,1 / 2), the vertical line is y = - 2x + 5 / 2, when y = 0, x = 5 / 4