Question #59cc5

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Answer 1 · 2017-02-16T11:42:30

# D(x,y)=D(-9,1)#.

Name the given points #A(3,4), B(5,-4) and C(-7-7)#.

Using the Distance Formula, we haave,

#AB^2=(3-5)^2+(4-(-4))^2=4+64=68#

#BC^2=144+9=153, and, AC^2=221#.

We conclude that, #AB^2+BC^2=AC^2#

So, we have, #m/_B=90^@," &, in the Rectangle "ABCD, BD" is the other Diagonal"#.

Recall that a Rectangle is also a Parallelogram, its diagonals bisect

each other; i.e., to say that, #AC and BD# bisect each other.

In other words,

The mid-pt. of #AC="mid-pt. of "BD.#

If, #D=D(x,y),# then, using the Formula for Mid-pt. of Sgmt.,

#((3-7)/2,(4-7)/2)=((5+x)/2,(-4+y)/2)#

#rArr D(x,y)=D(-9,1)" is the fourth vertex of the Rectangle "ABCD#.

Enjoy Maths.!