Question

x minus y + 2 equal to zero and 4 x minus y - 4 equal to zero also calculate the area of triangle formed by the shown draw and x-axis class 10th​

Answer 1

x=2

y=4

Step-by-step explanation:

x-y+2=0

x-y= -2

similarly

4x-y-4 = 0

4x-y = 4

subtracting equation 1 from equation 2 we get

3x = 6

x = 2

putting value of x in equation 1 we get

x-y = -2

2-y = -2

-y = -2 -2

-y = -4

y = r

Answer 2

The area of triangle is 6 square units.

Please refer to the picture for the graph

GIVEN

Linear equations -

$x - y + 2 = 0$

$4x - y - 4 = 0$

TO FIND

The Area of the triangle formed.

SOLUTION

We can simply solve the above problem as follows ;

We are given a linear equation -

x - y + 2 = 0

We can also write it as,

y = x+2

So,

When,

x = 0

y = 0+2 = 2

When,

x = -2

y = -2+2 = 0

Similarly,

The linear equation, 4x-y-4 = 0 can be written as, y = 4x-4

When,

x = 0; y = - 4

x = 1; y = 0

Plotting the graph, using the solution of (x,y) as -

(x₁,y₁) = (0,2.)

(x₂,y₂) = (-2,0)

(x₃,y₃) = (0,-4)

(x₄,y₄) = (1,0)

The vertices of ΔABC are-

A = ( -2,0)

B = (1,0)

C = (2,4)

Applying the distance formula-

$AB = \sqrt{1 - ({ - 2}^{2}) + ({0 - 0})^{2} }$

$AB = \sqrt{ {3}^{2} }$

AB = 3

We know That,

Area of the triangle = (1/2)× base × height

Area of ΔABC =

$\frac{1}{2} \times 3 \times 4 = 6 \: square \: units$

Hence, The area of the triangle is 6 square units.

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