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Luda [366]
3 years ago
8

If the vertices of a square are A(–2, 4), B(4, 4), C(4, –2), and D(–2, –2), what are the coordinates of the point where the diag

onals intersect?

Mathematics
1 answer:
Komok [63]3 years ago
8 0
Check the picture below.

notice, is just a 6x6 square, therefore its diagonals will cut each other in half, thus they both will meet at their midpoint, so let's check the midpoint for AC then,

\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&A&(~{{ -2}} &,&{{ 4}}~) 
%  (c,d)
&C&(~{{ 4}} &,&{{ -2}}~)
\end{array}\qquad
%   coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left( \cfrac{4-2}{2}~~,~~\cfrac{-2+4}{2} \right)\implies \left( \cfrac{2}{2}~~,~~\cfrac{2}{2} \right)\implies (1,1)

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