Question

B is the midpoint of ACand E is the midpoint of BD. If A(-9, -4), C(-1, 6), and E(-4, -3), find

the coordinates of D.

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Answer 1

`Solution,\\Midpoint of coordinates (a ,b) and (c,d) is given by:\\(x,y) = ((a+b)/(2) , (c+d)/(2)) \\Therefore, coordinate of B is\\((-9-1)/(2),(-4+6)/(2)) = ((-8)/(2),(2)/(2)) = (-4 , 1)`

`Similarly,\\E(4, -3) = ((-4+x)/(2),(1+y)/(2)) where, (x,y) are the coordinates of D\\or, 4=(x-4)/(2) and -3 = (y+1)/(2)\\or, 8 = x - 4 and -6 = y+1\\or, x= 12 and y = -5\\Therefore, the coordinates of D are (12,-5)`