Two coordinates of rectangle ABCD are A(-3, 4), C(7,12) Coordinate B is (-3, ?)

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Answer 1 · 2018-04-03T19:47:16

(-3,12)

B is directly above A and must be horizontal with C so it is (-3,12)

Answer 2 · 2018-04-04T07:36:33

# B(-3,12)#.

Let in the rectangle #ABCD, A(-3,4), B(-3,y) and C(7,12)#.

But, in the rectangle #ABCD#, we have,

#color(red)(AB^2)+color(blue)(BC^2)=color(green)(AC^2)#.

Therefore, by the distance formula, we get,

#color(red){(-3-(-3))^2+(4-y)^2}+color(blue){(-3-7)^2+(y-12)^2}#

#=color(green){(-3-7)^2+(4-12)^2}#.

#:.color(red)(0+16-8y+y^2)+color(blue)(100+y^2-24y+144)=color(green)(100+64)#.

#:. 2y^2-32y+96=0, i.e., y^2-16y+48=0#.

#:. (y-12)(y-4)=0#.

#:. y=12, or, y=4#.

But, #y=4 rArr B(-3,y)=B(-3,4)=A(-3,4)#.

#:. y!=4," leaving, "B(-3,y)=B(-3,12)#,

as Respected Mark D. has readily obtained!

Enjoy Maths.!