It is known that the image of the first-order function y = - 12x + 4 intersects with the x-axis and y-axis at points a and B respectively. The edge AC of the trapezoid aobc is 5. (1) find the coordinates of point C; (2) if points a and C are on the image of the first-order function y = KX + B (K and B are constants, and K < 0), find the analytic expression of the first-order function

It is known that the image of the first-order function y = - 12x + 4 intersects with the x-axis and y-axis at points a and B respectively. The edge AC of the trapezoid aobc is 5. (1) find the coordinates of point C; (2) if points a and C are on the image of the first-order function y = KX + B (K and B are constants, and K < 0), find the analytic expression of the first-order function

(1) In trapezoidal aobc, OA = 8, OB = 4, AC = 5, when AC ∥ ob (as shown in Fig. 1), the coordinates of point C are (8,5). When BC ∥ OA (as shown in Fig. 2), set point C (x, 4). ∥ AC = 5, ∥ (X-8) 2 + (4-0) 2 = 52, ∥ X1 = 5, X2 = 11, then the coordinates of point C are (5,5) The coordinates of point C are (8,5) or (5,4) or (11,4); (2) ∵ points a and C are on the image of the first-order function y = KX + B (k < 0); (8,5) and (11,4) do not conform to the problem. Only when C is (5,4), K < 0, ∵ 0 = 8K + B4 = 5K + B, ∵ k = − 43b = 323