If we know that the images of the linear functions y = 3 / 2x + m and y = 1 / 2x + n pass through point a (2,0) and intersect with y axis at two points B and C respectively, then the area of △ ABC is

If we know that the images of the linear functions y = 3 / 2x + m and y = 1 / 2x + n pass through point a (2,0) and intersect with y axis at two points B and C respectively, then the area of △ ABC is

 
 
Analysis: first, substitute (- 2,0) into the first-order functions y = & nbsp; 3 / 2 & nbsp; X + m and y = - 3 / 2 & nbsp; X + n respectively to get the value of M and N, then get the analytic expressions of the two functions; then get the coordinates of B and C; finally, get the area of △ ABC according to the area formula of triangle
The images of y = 3 / 2 & nbsp; X + m and y = - 3 / 2 & nbsp; X + n all pass through point a (- 2,0),
So we can get 0 = 3 / 2 × (- 2) + m, 0 = - 3 / 2 × (- 2) + n,
∴m=3,n=-3,
The expressions of the two functions are y = 3 / 2 & nbsp; X + 3, y = - 3 / 2 & nbsp; x-3,
The intersection points of y = 3 / 2 & nbsp; X + 3 and y = - 3 / 2 & nbsp; x-3 and Y axis are B (0,3), C (0, - 3), respectively,
S△ABC=1/2BC•AO=1/2×6×2=6．
 
 
 
Comments: this question mainly examines the relationship between the function analytic formula and the image. The point on the image of the function satisfies the function analytic formula, on the contrary, the point satisfying the analytic formula must be on the image of the function