Question

If the midpoint of point A on the x=3 line and point B on the y=-2 line is C(-2,0), what is the sum of the ordinate of point A and the abscissa of point B?

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Cristian

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A lies on the line x=3 therefore let coordinates of A be (3,a) and B lies on the line y=-2 therefore let coordinates of B be (b,-2).
Therefore, coordinates of midpoint of AB is C i.e. \left(\frac{\left(3+b\right)}{2},\frac{\left(a-2\right)}{2}\right)
Given the coordinates of C are (-2,0)
Therefore, \frac{\left(b+3\right)}{2}=-2 and \frac{\left(a-2\right)}{2}=0
By solving we get, a=2 and b=-7
Therefore the required answer is (a+b)=2-7=-5

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