Question

若点P到点A(0,1)、B（7,2）及X轴的距离相等,则P点的坐标是?

Answer 1

设点P(m,n)

则：P到x轴距离为|n|

AP=n

(m-0)²+(n-1)²=n² (1)

m²+n²-2n+1=n²

n=(m²+1)/2 (3)

BP=n

(m-7)²+(n-2)²=n² (2)

m²-14m-4n+53=0

m²-14m-4(m²+1)/2+53=0

m²+14m-51=0

(m-3)(m+17)=0

m=3; n=5

或

m=-17; n=145

P点的坐标是(3,5)或(-17,145)