If the pointA(x,2)is equidistant from the point B(8,-2)and C(2,-2),find the value of x .Also,find the length of AB

Asked by Anas.123 | 10th Sep, 2018, 12:55: PM

Expert Answer:

Since Point A is equidistant from the point B and C.
Therefore,
AB = AC
Squaring on both the sides,
begin mathsize 16px style AB squared space equals space AC squared
rightwards double arrow left parenthesis straight x space minus space 8 right parenthesis squared space plus space left parenthesis space 2 space plus space 2 right parenthesis squared space equals space left parenthesis straight x space minus space 2 right parenthesis squared space plus space left parenthesis space 2 space plus space 2 right parenthesis squared
rightwards double arrow straight x squared space minus space 16 straight x space plus space 64 space plus space 16 space equals space straight x squared space minus space 4 straight x space plus space 4 space plus space 16
rightwards double arrow negative 12 straight x space equals space minus 60
rightwards double arrow straight x space equals space 5
Therefore comma space the space Point space space straight A left parenthesis 5 comma space 2 right parenthesis.
rightwards double arrow AB thin space equals space square root of open parentheses 5 space minus space 8 close parentheses squared space plus space open parentheses 2 space plus space 2 close parentheses squared end root space space space equals space square root of 25 space equals space 5 space units end style
 

Answered by Yasmeen Khan | 12th Sep, 2018, 05:55: PM

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