Question

In each of the following figures ABCD is a parallelogram.
A = 4x + 20
B = 7y
C = 0
D = 6x + 3y - 8

In each case given above , find the values of x and y

Answer 1

Answer:

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 1:

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

       Class_11_Straight_Lines_Graph1                        

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

Accordingly, 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 – y2)|

Therefore, area of ∆ABC = (1/2)|-4(7 + 5) + 0(-5 - 5) + 5(5 - 7)|

                                            = (1/2)|-4 * 12 – 5 * 2|

                                            = (1/2)|-48 – 10|

                                            = (1/2)|-58|

                                            = 58/2

                                            = 29 unit2      

Area of ∆ACD = (1/2)|-4(-5 + 2) + 5(-2 - 5) + (-4)(5 + 5)|

                        = (1/2)|4 * 3 – 5 * 7 – 4 * 10|

                        = (1/2)|12 -35 – 40|

                        = (1/2)|-63|

                        = 63/2  unit2      

Thus, area(ABCD) = 29 + 63/2 = (58 + 63)/2 = 121/2 unit2

Step-by-step explanation:

more of length sorry but definetly helps you

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