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Question
M (-2, y) is a point equidistant from the points A(5,7) and B(3,-4). Find the value of y.
M (-2, y) is a point equidistant from the points A(5,7) and B(3,-4). Find the value of y.
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Solution
The correct option is A
Point M (-2, y) is equidistant from the points A (5, 7) and B(3 , -4)
Distance AM = Distance BM
⇒√((xa−xm)2+(ya−ym)2) = √((xb−xm)2+(yb−ym)2))⇒(5−(−2))2+(7−y)2=(3−(−2))2+(−4−y)2⇒49+49−14y+y2=25+16+8y+y2⇒22y=57⇒y=5722
Point M (-2, y) is equidistant from the points A (5, 7) and B(3 , -4)
Distance AM = Distance BM
⇒√((xa−xm)2+(ya−ym)2) = √((xb−xm)2+(yb−ym)2))⇒(5−(−2))2+(7−y)2=(3−(−2))2+(−4−y)2⇒49+49−14y+y2=25+16+8y+y2⇒22y=57⇒y=5722
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