Question

已知点O(0,0),A(2,2),B(1,a),三角形ABO的面积等于5,求a值

Answer 1

过O,A的直线方程LOA:

x-y=0

|OA|=(2^2+2^2)^(1/2)=4*2^(1/2)

B(1,a)到LOA的距离d=|1-a|/(2^(1/2))

5=|OA|*d/2=4*2^(1/2)*|1-a|/(2^(1/2))/2=5

|1-a|=5/2

a=7/2或a=-3/2