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Coordinate Geometry — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsCoordinate Geometry4 Marks
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.
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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 × BC) = (6 × 2)sq. units = 12sq. units Hence, the area of rectangle ABCD 12 square units.

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