=Answer:
The coordinate of A is (8,-12)
Step-by-step explanation:
Let the coordinate of A be (x1, y1)
and the coordinates of M is (3,-4) and B is (-2,4)
SInce the midpoint of AB is M
Therefore,
Midpoint of AB = [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\[/tex]
[tex](3,-4) = (\frac{x_{1}-2}{2},\frac{y_{1}+4}{2} )\\[/tex]
Comparing both sides, we get:
[tex]3=\frac{x_{1}-2}{2}\\ 6=x_{1}-2\\x_{1}=6+2\\x_{1}=8[/tex] [tex]-4=\frac{y_{1}+4}{2} \\-8=y_{1}+4\\-8-4=y_{1}\\y_{1}=-12[/tex]
Therefore the coordinate of A is (8,-12)
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