If the point c(-2,3) is equidistant from the points A(3,-1) and B(x, 8), find the values of x. Also, find the distance BC.
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Given: Points C(−2,3) is equidistant from points A(3,−1) and B(x,8).
Then,
CA=CB
or CA2=CB2
CB2=(x+2)2+(8−3)2
CA2=(3+2)2+(−1−3)2
(x+2)2+(8−3)2=(3+2)2+(−1−3)2
(x+2)2+52=52+(−4)2
x2+4x+4+25=25+16
x2+4x+29−41=0
x2+4x−12=0
x2+6x−2x−12=0
x(x+6)−2(x+6)=0
(x+6)(x−2)=0
This implies: x=2 or x=−6
Therefore: AC=
units.
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