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Question

If M (c, -1) is a point equidistant from the points A(1, 3) and B(-5, -5), then the value of c is.

A
2
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B
-2
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C
0
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Solution

The correct option is B -2
Given that point M is equidistant from points A(1, 3) and B(-5, -5).
AM = BM

Distance between two points (x1,y1) and (x2,y2)
=((x2x1)2+(y2y1)2

AM = BM
(c1)2+(13)2
=(c(5))2+(1(5))2
(c1)2+16=(c+5)2+16(c1)2+16=(c+5)2+16(c1)2=(c+5)2c2+12c=c2+25+10c12c=24c=2

The value of c is -2.

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