Draw a quadrilateral in the Cartesian plane, whose vertices are (- 4, 5), (0, 7), (5 - 5) and (- 4, - 2) . Also, find its area

Solution:

Let ABCD be the given quadrilateral with vertices A(- 4, 5), B (0, 7), C (5, - 5) and D (- 4, - 2).

Then, by plotting A, B, C and D on the Cartesian plane and joining AB, BC, CD and DA, the given quadrilateral can be drawn as

To find the area of quadrilateral ABCD, we draw one diagonal, say AC.

Accordingly, ar (ABCD) = ar (ΔABC ) + ar (ΔACD)

We know that the area of a triangles whose vertices are ( x₁, y₁), ( x₂ , y₂) and ( x₃, y₃) is

1/2 |x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂)|

Therefore,

ar (ΔABC) = 1/2 |- 4 (7 + 5) + 0 (- 5 + 5) + 5(5 - 7)|

= 1/2 |- 48 + 0 - 10|

= 1/2 | - 58|

= 1/2 (58)

= 29

ar (ΔACD) = 1/2 |(- 4)(- 5 + 2) + 5(- 2 - 5) + (- 4)(5 + 5)|

= 1/2 |12 - 35 - 40|

= 1/2 |- 63|

= 1/2 (63)

= 63/2

Thus,

ar (ABCD) = ar (ΔABC ) + ar (ΔACD)

= 29 + 63/2 sq. unit

= (58 + 63)/2 sq. unit

= 121/2 sq. unit

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NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.1 Question 1

Draw a quadrilateral in the Cartesian plane, whose vertices are (- 4, 5), (0, 7), (5 - 5) and (- 4, - 2) . Also, find its area

Summary:

The area of the quadrilateral mentioned above with vertices A(- 4, 5), B (0, 7), C (5, - 5), and D (- 4, - 2) is 121/2 sq. unit