Question
Three vertices of a rectangle $ABCD$ are $A(3, 1), B(-3, 1)$ and $C(-3, 3)$. plot these points on a graph paper and find the coordinates of the fourth vertex $D$. Also find the area of rectangle $ABCD$.
✓
Answer
Let $A(3, 1), B(-3, 1)$ and $C(-3, 3)$ be three vertices of a rectangle $ABCD$.
Let the $y$-axis cut the rectangle $ABCD$ at the points $P$ and $Q$ respectively. (Image)
Abscissa of $D$ = Abscissa of $A = 3.$
Ordinate of $D$ = ordinate of $C = 3.$
$\therefore$ coordinates of $D$ are $(3, 3). AB = (BP + PA) = (3 + 3)$ units $= 6$ units.
$BC = (OQ - OP) = (3 - 1)$ units$ = 2$ units.
$Ar($rectangle $ABCD) $
$= (AB \times BC) = (6 \times 2)$sq. units
$= 12$sq. units
Hence, the area of rectangle $ABCD$ $12$ square units.
Let the $y$-axis cut the rectangle $ABCD$ at the points $P$ and $Q$ respectively. (Image)
Abscissa of $D$ = Abscissa of $A = 3.$
Ordinate of $D$ = ordinate of $C = 3.$
$\therefore$ coordinates of $D$ are $(3, 3). AB = (BP + PA) = (3 + 3)$ units $= 6$ units.
$BC = (OQ - OP) = (3 - 1)$ units$ = 2$ units.
$Ar($rectangle $ABCD) $
$= (AB \times BC) = (6 \times 2)$sq. units
$= 12$sq. units
Hence, the area of rectangle $ABCD$ $12$ square units.
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