Q. 383.7( 3 Votes )

# The three vertices of a rectangle ABCD are A(3, 2), B(–2, 2) and C(3, –3). Plot these points on a graph paper and find the coordinates of D. Also, find the area of rectangle ABCD.

Answer :

Let the three vertices of rectangle ABCD be A (3, 2), B (-2, 2) and D (3, -3)

Now, on plotting these points on the graph paper and by joining the points we get:

A, B and D lie in different quadrants

Let us assume D be the fourth vertex of the rectangle

∴ Abscissa of C = Abscissa of B = - 2

And, Ordinate of C = Ordinate of D = - 3

Hence, Coordinate of the fourth vertex, C = (-2, -3)

Let y-axis cut AB and CD at point L and M respectively

∴ AB = (BL + LA)

= (2 + 3)

= 5 units

∴ Area of rectangle ABCD = AB × AB

= 5 × 5

= 25 square units

Hence, the area of the rectangle ABCD is 25 square units

Rate this question :

Without plotting the points indicate the quadrant in which they will lie, if

(i) ordinate is 5 and abscissa is – 3

(ii) abscissa is – 5 and ordinate is – 3

(iii) abscissa is – 5 and ordinate is 3

(iv) ordinate is 5 and abscissa is 3

NCERT Mathematics ExemplarIn Fig. 3.6, LM is a line parallel to the y-axis at a distance of 3 units.

(i) What are the coordinates of the points P, R and Q?

(ii) What is the difference between the abscissa of the points L and M?

NCERT Mathematics Exemplar

Which of the following points lie on y-axis?

A(1, 1), B(1, 0), C(0, 1), D(0, 0), E(0, – 1), F(– 1, 0), G(0, 5), H(– 7, 0), I(3, 3)

NCERT Mathematics ExemplarPlot the points (x, y) given by the following table:

Draw the graph of the equation,

RS Aggarwal & V Aggarwal - MathematicsIn the adjoining figure, name :

(i) Six Points

(ii) Five Line Segments

(iii) Four rays

(iv) Four lines

(v) Four collinear points

RS Aggarwal & V Aggarwal - MathematicsWhich point does not lie in any quadrant?

RS Aggarwal & V Aggarwal - MathematicsPlot the points (x, y) given by the following table.

Use scale 1 cm = 0.25 units

NCERT Mathematics Exemplar

Draw the graph of the equation,

RS Aggarwal & V Aggarwal - MathematicsDraw the graph of the equation,

RS Aggarwal & V Aggarwal - Mathematics