Question

[3]
b) Find the slope and the y-intercept of the line 4x – 3y = 2.
c) A triangle is formed by the lines x + 2y – 3 = 0,3x – 2y + 7 = 0 and
y + 1 = ​

Answer 1

Step-by-step explanation:

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