Straight Lines – Exercise 10.1 – Class XI

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Breath Math

  1. 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).

Now let us plot A, B, C, and D on the Cartesian plane and joining AB, BC, CD, and DA, the given quadrilateral can be drawn as

Straight lines - Exercise 10.1 - Class XI

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

Thus, area (ABCD) = area (∆ABC) + area (∆ACD)

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

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

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