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telo118 [61]
3 years ago
15

The endpoints of a side of rectangle ABCD in the coordinate plane are at A (2, 11) and

Mathematics
1 answer:
Doss [256]3 years ago
5 0

ANSWER

2y-x-20=0


or

y=\frac{1}{2}x+10


<u>EXPLANATION</u>

Let the rectangle be oriented as shown in the diagram.

The line segment AD passes through A(2,11).


All we need now is the slope of AD then we can find its equation.


Since AD is perpendicular t AB, we determine the slope of AB and then use it to find the slope of AD.


Slope_{AB}=\frac{1-11}{7-2}



Slope_{AB}=\frac{-10}{5}=-2


The slope of AD is the negative reciprocal of the slope of AB because they are perpendicular.

Slope_{AD}=\frac{-1}{-2}=\frac{1}{2}


The equation of AD is given by;


y-y_1=m(x-x_1)


y-11=\fra[1}{2}(x-2)


Multiplying through by 2 gives,


2y-22=(x-2)


2y-x-22+2=0


2y-x-20=0


or

y=\frac{1}{2}x+10














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