Question

X - Y = 4 Х -1 - 0 y 0 O -4 (x, y) (0, -4) $​

Answer 1

Answer:

anjaligodara2003

anjaligodara2003

25.12.2018

Math

Secondary School

answered

Draw the graph of pair of linear equations x-y+2=0 and 4x-y-4=0. calculate the area of triangle formed by lines so drawn and x-axis.

2

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JeanaShupp

Given: Linear equation x-y+2=0 and 4x-y-4=0.

To find : Area of triangle formed by lines so drawn and x-axis

Step-by-step explanation:

1) x-y+2=0

if x = 0

0-y+2=0\\\\\Rightarrow y= 2

so (0,2) is the solution

Now if y=0

x-0+2=0\\\\\Rightarrow x=-2

Hence, (-2,0) is the solution

Similarly

4x-y-4=0

(0,-4) and (1,0) are the solution

Attached graph

Now as we can see from the graph

The coordinate of triangle formed by lines so drawn and x-axis are (-2,0),(1,0), (2,4)

Now as we know area of triangle is given by

Area=\dfrac{1}{2} |x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|

where

(x_1,y_1)=(-2,0) ,(x_2,y_2)=(1,0), (x_3,y_3)=(2,4)

So we have

Area = \dfrac{1}{2} |-2(0-4)+1(4-0)+2(0-0)|\\\\\Rightarrow Area = \dfrac{1}{2} |8+4|=\dfrac{12}{2} =6