Parabola of elementary third quadratic function It is known that there is a point C (0,2) d (4,6) on the x-axis in the plane Cartesian coordinates, and there is a point a whose distance from point C and point D is the smallest Finding the coordinates of point a

Because make AC, Da connection shortest
So point a is at the midpoint of line CD
Let a straight line pass through points c and D
The analytic formula is y = x + 2
The length of CD, AC and ad can be obtained by the formula of distance between two points
Let a (a, b)
Because y = x + 2
So a (a, a + 2)
Because (A-0) ^ 2 + (b-2) ^ 2 = (A-4) ^ 2 + (B-6) ^ 2 (because AC = AD)
Then the a coordinate can be obtained,

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