find a point in y- axis which is equidistant from the points A (7,6) and B (-3 ,4).
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Given points A(7,6) and B(-3,4)
Let the point be P(0,y) [we know that point on y-axis is (0,y)]
So, AP=PB and AP2=PB2
⇒(y-7)2+(0-6)2=(y+3)2+(0-4)2
y2+49-14y + 36=y2+9+6y + 16
49-9+36-16=6y+14y
40+20=20y
60/20=y
⇒y=3
Hence, point on x-axis which is equidistant from the points A(7,6) and B(-3,4) is (0,3).-----Ans.
Let the point be P(0,y) [we know that point on y-axis is (0,y)]
So, AP=PB and AP2=PB2
⇒(y-7)2+(0-6)2=(y+3)2+(0-4)2
y2+49-14y + 36=y2+9+6y + 16
49-9+36-16=6y+14y
40+20=20y
60/20=y
⇒y=3
Hence, point on x-axis which is equidistant from the points A(7,6) and B(-3,4) is (0,3).-----Ans.
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