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Question

Find a point on the x- axis which is equidistant from the points (7, 6) and (-3, 4).

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Solution

Given points A(7,6) and B(-3,4)
Let the point be P(x,0) [we know that point on x-axis is (x,0)]
So, AP=PB and A P squared equals P B squared
left parenthesis x minus 7 right parenthesis squared plus left parenthesis 0 minus 6 right parenthesis squared equals left parenthesis x plus 3 right parenthesis squared plus left parenthesis 0 minus 4 right parenthesis squared space x squared plus 49 minus 14 x space plus space 36 equals x squared plus 9 plus 6 x space plus space 16
49 minus 9 plus 36 minus 16 equals 6 x plus 14 x space 40 plus 20 equals 20 x space 60 over 20 equals x space x equals 3
Hence, point on x-axis which is equidistant from the points A(7,6) and B(-3,4) is (3,0)

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