Known: a (0,1), B (2,0), C (4,3) (1) find the area of △ ABC (2) set point P on the coordinate axis, and the area of △ ABP and △ ABC

Known: a (0,1), B (2,0), C (4,3) (1) find the area of △ ABC (2) set point P on the coordinate axis, and the area of △ ABP and △ ABC

(1) Connect AB, AC, BC ∵ a (0,1) B (2,0) C (4,3) ∵ Ao = 1, Bo = 2, CD = 3, OD = 4, BD = 2 ∵ s △ AOB = 1 / 2 * AO * Bo = 1 / 2 * 1 * 2 = 1s △ CBD = 1 / 2 * BD * DC = 1 / 2 * 2 * 3 = 3S ladder aodc = 1 / 2 * od * (AO + CD) = 1 / 2 * 4 * (1 + 3)

If point P is a moving point on the ABC side of a triangle with area 4, how many points satisfy the ABP area = 1?

A:
There are two
Divide AC and BC into four equal parts. The points near a on AC and B on BC are all the points

As shown in the figure, given the points a (2,0), B (0,1), C (2,3), if there is a point P (m, 12) in the first quadrant, and the area of △ ABP is equal to the area of △ ABC, find the value of M

Let the analytic formula of line AB be y = KX + B (K ≠ 0), ∵ point a (2,0), B (0,1), ∵ 2K + B = 0b = 1, the solution is k = − 12b = 1, ∵ the analytic formula of line AB is y = - 12x + 1. Let the intersection line of parallel lines of line AB through point C be y = 12 at point P. let the analytic formula of line CP be y = - 12x + B, ∵ C (2,3), ∵ 3 = - 12 × 2 + B, the solution is b = 4, ∵ the analytic formula of line CP is y = - 12x + 4, ∵ when y = 12, x + 4= 7，∴m=7．

If point P is a moving point on the edge of △ ABC of area 4, then point P with △ ABP area equal to 1 has______ One

Let the height of AB side in △ ABC be h, then the height of AB side in △ ABP is 14h, and the distance to AB is 14h from the area formula. As the parallel line p1p2 with the distance to ab of 14h, we can see that there are two points satisfying the condition, such as point P1 and point P2 in the figure