Given 2 points A(a,b) and M(k,l), the distance between them is found by the formula:
[tex]|AM|= \sqrt{ (a-k)^{2} + (b-l)^{2} } [/tex]
Let (k, l)=(2, 3), substituting in the above formula:
[tex]12= \sqrt{ (a-2)^{2} + (b-3)^{2} }[/tex]
[tex](a-2)^{2} + (b-3)^{2}=12 ^{2}=144 [/tex]
check each of the pairs given:
for (a, b)=(14, 15):
[tex](a-2)^{2} + (b-3)^{2}=(14-2)^{2} + (15-3)^{2}=(12)^{2} + (12)^{2}=288[/tex]
for (a, b)=(2, -9):
[tex](2-2)^{2} + (-9-3)^{2}=0+(-12)^{2}=144[/tex]
for (a, b)=(-2, -3):
[tex](-2-2)^{2} + (-3-3)^{2}=(-4)^{2} + (-9)^{2}=16+81=97[/tex]
for (a, b)=(-9, 2):
[tex](-9-2)^{2} + (2-3)^{2}=(-11)^{2} + (-1)^{2}=121+1=122[/tex]
Answer: (2, -9)
