The vertex o (0,0), a (2,1), B (10,1) of triangle OBC, the line CD is perpendicular to the X axis and bisects the area of triangle ABC. If D (x, 0), then the value of X is

The vertex o (0,0), a (2,1), B (10,1) of triangle OBC, the line CD is perpendicular to the X axis and bisects the area of triangle ABC. If D (x, 0), then the value of X is

1. Calculate the distance AE from a to the straight line Bo, the equation of Bo: x-10y = 0, so AE = 8 / root 101, the area of triangle ABO can be obtained as s = AE · Bo / 2 = 8
2. Because the coordinate of D is (m, 0) and CD is perpendicular to X axis, then the coordinate of the intersection point C of CD and ab is: (m, 1)
3. CD = 10-m, let CD and ab intersect point F, CF = k, then DF = 1-k, OD = M
So: from the similar triangle, we can get: DB: od = CF: DF
That is (10-m): M = k: 1-k
So we can find the relationship between K and M: k = (10-m) / 10
Because ABC is divided into two parts
So the area of triangle DBF is 1, that is, (10-m) · (10-m) / 10.2 = 2
The solvable M = 10 + - radical 20
Among them, 10 + radical 20 > 10 is not appropriate
therefore
M = 10-radical 40 = 10-2 radical 10

As shown in the figure, the vertex of △ OAB is O (0,0), a (2,1), B (10,1), the straight line CD ⊥ X axis, and the area of △ 0ab is bisected. If the coordinate of point D is (x, 0), find the value of X

Let y = KX (K ≠ 0), ∵ B (10,1), ∵ 1 = 10K for OB, and the solution is k = 110. Let y = 110x, ∵ D (x, 0), ∵ f (x, X10), ∵ EF = 1-x10, EB = 10-x, ab = 10-2 = 8, ∵ s △ bef = 12 × 10 − X10 × (10-x) = (10 − x) 220, ∵ s △ AOB = 12 × 8 × 1 = 2 × (10 − x) 220, and the solution is x = 10-210

Find a point P on the x-axis so that the area of the triangle with points a (1,2), B (3,4) and P as vertices is 10

Let | ab | = 22, and the equation of the straight line AB is y − 24 − 2 = x − 13 − 1 {x − y + 1 = 0. (3 points) in △ PAB, let the height of the edge of AB be h, then 12 · 22h = 10 {H = 52, (7 points) let P (x, 0), then the distance from P to AB is | x + 1 | 2, so | x + 1 | 2 = 52, (10 points) the solution is x = 9, or x = - 11. (11 points) so, the coordinates of the point are (9, 0), or (- 11, 0) ）(12 points)

The three triangles obtained by connecting a point in the triangle with three vertices divide the area of the original triangle into three equal parts. What is the point of the triangle?

Central point