In the coordinate plane, three vertices of rectangle ABCD are A(0, 0), B(0, a), and D(b, 0). What are the coordinates of point C?

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In the coordinate plane, three vertices of rectangle ABCD are A(0, 0), B(0, a), and D(b, 0). What are the coordinates of point C?

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Answer 1 · 2017-02-11T07:06:10

Coordinates of $C$ $C$ are $(b, a)$ $(b,a)$

Explanation:

As $A (0, 0)$ $A(0,0)$ and $B (0, a)$ $B(0,a)$ have abscissa as $0$ $0$ , they fall on $y$ $y$ -axis. Similarly $A (0, 0)$ $A(0,0)$ and $D (b, 0)$ $D(b,0)$ have ordinate as $0$ $0$ , they fall on $x$ $x$ -axis.

As such $B C$ $BC$ || $A D$ $AD$ i.e. parallel to $x$ $x$ axis and as such $B$ $B$ and $D$ $D$ must have common ordinate i.e. $a$ $a$ .

Also $C D$ $CD$ || $A B$ $AB$ i.e. parallel to $y$ $y$ axis and as such $C$ $C$ and $D$ $D$ must have common abcissa i.e. $b$ $b$ .
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Hence, coordinates of $C$ $C$ are $(b, a)$ $(b,a)$

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In the coordinate plane, three vertices of rectangle ABCD are A(0, 0), B(0, a), and D(b, 0). What are the coordinates of point C?

1 Answer

Explanation:

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