Three points

Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC
What is the value of k?

Correct answer:

k1 =  7
k2 =  -17

Step-by-step explanation:

d=AB d=(39)2+(5(10))2=13 d2 = (32)2+(5k)2  132=(32)2+(5k)2  k210k+119=0 k2+10k119=0  a=1;b=10;c=119 D=b24ac=10241(119)=576 D>0  k1,2=2ab±D=210±576 k1,2=210±24 k1,2=5±12 k1=7 k2=17  k1=7

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