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locus
2007-04-16 8:12 am
A(-4,2) and B(1,-3) are two points .C is a point on the y-axis such that AC=CB. Find the coordinates of C.?
回答 (2)
2007-04-16 5:37 pm
✔ 最佳答案
Let C = (0, y)AC = CB
(0+4)^2 + (y-2)^2 = (1-0)^2 + (-3-y)^2
16 + y^2 - 4y + 4 = 1 + y^2 + 6y + 9
10y = 10
y = 1
Therefore, coordiantes of C is (0, 1)
*C lies on y-axis. Therefore x-coordinate of C MUST BE 0.
2007-04-16 8:26 am
Let ( 0 , y ) be coordinates of C .
AC = CB
root [ ( -4 - 0 )^2 + ( 2 - y )^2 ] = root [ ( 1 - 0 )^2 + ( -3 - y )^2 ]
16 + ( 2 - y )^2 = 1 + ( -3 - y )^2
16 + 4 - 4y + y^2 = 1 + 9 + 6y + y^2
20 - 4y = 10 + 6y
10 = 10y
y = 1
Therefore , the coordinates of C is ( 0 , 1 ) .
AC = CB
root [ ( -4 - 0 )^2 + ( 2 - y )^2 ] = root [ ( 1 - 0 )^2 + ( -3 - y )^2 ]
16 + ( 2 - y )^2 = 1 + ( -3 - y )^2
16 + 4 - 4y + y^2 = 1 + 9 + 6y + y^2
20 - 4y = 10 + 6y
10 = 10y
y = 1
Therefore , the coordinates of C is ( 0 , 1 ) .
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