Draw a Quadrilateral in the Cartesian Plane Exercise Solutions 10.1 Chapter 10 Straight Lines Maths Class 11 NCERT

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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.

Answer

Draw a Quadrilateral ABCD whose vertices are A (–4, 5), B (0, 7), C (5, –5), and D (–4, –2).

Area of quadrilateral ABCD = area of ∆ABC + area of ∆ACD

Relate the coordinate of ∆ ABC, A (–4, 5), B (0, 7), C (5, –5) with (x1, y1), (x2, y2), and (x3, y3) and use formula

[ = frac{1}{2}|{x_1}({y_2} - {y_3}+{x_2}({y_3} –{y_1} )+ +{x_3}({y_1} –{y_2} |]

Plug the values, we get

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

=1/2|-4(12 +0 + 5(-2)|

=1/2|-48 -10|

=1/2 (58)

=29 unit²

Relate the coordinate of ∆ ABC, A (–4, 5), C (5, –5) and D (–4, –2). with (x1, y1), (x2, y2), and (x3, y3) and use formula

[ = frac{1}{2}|{x_1}({y_2} - {y_3}+{x_2}({y_3} –{y_1} )+ +{x_3}({y_1} –{y_2} |]

Area of ∆ACD

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

= ½ |-4(-3) +5(-7) +(-4)(10)|

=1/2|12 -35 -40|

=1/2|-63|

= 63/2 unit²

Total area of quadrilateral (ABCD) = 29+ 63/2 = 121/2 unit²

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