A(-4,0)；B（2,4）①求线段AB与y轴的交点点C的坐标.②点P在X轴,S△ABP=20,求点P的坐标.③点P在y轴已知：A(-4,0)；B（2,4）求：①求线段AB与y轴的交点点C的坐标.②点P在X轴,S△ABP=20,求点P的坐标.③点

Question

A(-4,0)；B（2,4）①求线段AB与y轴的交点点C的坐标.②点P在X轴,S△ABP=20,求点P的坐标.③点P在y轴
已知：A(-4,0)；B（2,4）
求：①求线段AB与y轴的交点点C的坐标.
②点P在X轴,S△ABP=20,求点P的坐标.
③ 点P在y轴,S△ABP=30,求点P的坐标.

Answer 1

①
AB的方程(两点式):(y - 0)/(4 - 0) = (x + 4)/(2 + 4)
2x - 3y + 8 = 0
x = 0,y = 8/3
C(0,8/3) (-4 < 0 < 2,C在线段AB上)
②
P(p,0)
S = (1/2)|AP|*B的纵坐标
= (1/2)|p + 4|*4
= 2|p + 4| = 20
p = 6或p = -14
P(6,0)或(P(-14,0)
③
P(0,p)
S = S△APC + S△BPC
= (1/2)|CP|*|A的横坐标| + (1/2)|CP|*B的横坐标
= (1/2)*|p - 8/3|*4 + (1/2)|p - 8/3|*2
= 3|p - 8/3| = 30
p = 38/3或p = -22/3
P(0,38/3)或(0,-22/3)