Rectangle ABCD as vertices A(9, 3), B(9, 6), and C(2, 6). What are the coordinates of point D?

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Rectangle ABCD as vertices A(9, 3), B(9, 6), and C(2, 6). What are the coordinates of point D?

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Answer 1 · 2017-01-21T06:30:36

$D (2; 3)$ $D(2;3)$

Explanation:

Let's calculate the middle point of the diagonal AC: it will be te middle point of the diagonal BD.

$M = (\frac{x_{A} + x_{C}}{2}; \frac{y_{A} + y_{C}}{2}) = (\frac{9 + 2}{2}; \frac{3 + 6}{2}) = (\frac{11}{2}; \frac{9}{2})$ $M=((x_A+x_C)/2;(y_A+y_C)/2)=((9+2)/2;(3+6)/2)=(11/2;9/2)$

and

$M = (\frac{x_{B} + x_{D}}{2}; \frac{y_{B} + y_{D}}{2}) = (\frac{9 + x_{D}}{2}; \frac{6 + y_{D}}{2})$ $M=((x_B+x_D)/2;(y_B+y_D)/2)=((9+x_D)/2;(6+y_D)/2)$

then

$\frac{9 + x_{D}}{2} = \frac{11}{2}; x_{D} = 2$ $(9+x_D)/2=11/2; x_D=2$

and

$\frac{6 + y_{D}}{2} = \frac{9}{2}; y_{D} = 3$ $(6+y_D)/2=9/2; y_D=3$

$D (2; 3)$ $D(2;3)$

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Rectangle ABCD as vertices A(9, 3), B(9, 6), and C(2, 6). What are the coordinates of point D?

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