Question

The area of triangle formed by the lines 2x - y = 4; 2x + y = 4 and Y - axis is

Answer 1

Answer:

8 sq units

Step-by-step explanation:

The area of triangle formed by the lines 2x - y = 4; 2x + y = 4 and Y - axis

2x - y = 4    

2x + y = 4

y axis  (mean x = 0)

lets find intersection point between each pair

2x - y = 4     , 2x + y = 4

Adding both 4x = 8  => x = 2  & y = 0   ( 2, 0)

2x - y = 4     & y axis  (x = 0)

=> (0 , - 4)

2x + y = 4     & y axis  (x = 0)

=> (0 ,  4)

Points  (2, 0) , (0 , -4)  , (0 , 4)

Using coordinate formuls

Area of traingle =  (1/2)| (2(-4 - 4) + 0(4 - 0) + 0(0 - (-4)|

= (1/2) * 2 * 8

= 8

or by finding sides length

(2, 0) , (0 , -4) =  √2² + 4²  = √20

(2, 0) , (0 , 4) =  √2² + 4²  = √20

(0 , -4)  , (0 , 4) = 8

S = 4 + √20

Area = √S(S-A)(S-B)(S-C) = √(4 + √20)(4)(4)(√20 - 4)

= √(20 - 16)(4)(4)

= √64

= 8