Answer: The intersection of the line through (0, 1) and (4.3, 2) and the line through (2.1, 3) and (5.3, 0) is (3.392, 1.789).
Step-by-step explanation:
We know that the equation of a line that passes through two points (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Similarly , the equation of line that passes through (0, 1) and (4.3, 2) would be:
[tex](y-1)=\dfrac{2-1}{4.3-0}(x-0)[/tex]
[tex](y-1)=\dfrac{1}{4.3-}(x)[/tex]
[tex]4.3(y-1)=x[/tex]
[tex]4.3y-4.3=x-----(1)[/tex]
Equation of line that passes through (2.1, 3) and (5.3, 0) would be:
[tex](y-0)=\dfrac{3-0}{2.1-5.3}(x-5.3)[/tex]
[tex]y=\dfrac{3(x-5.3)}{-3.2}-----(2)[/tex]
To find the intersection point (x,y) , we substitute the value of y from (2)in (1) , we get
[tex]4.3(\dfrac{3(x-5.3)}{-3.2})-4.3=x[/tex]
[tex]-4.03125(x-5.3)-4.3=x[/tex]
[tex]-4.03125x+21.365625-4.3=x[/tex]
[tex]-4.03125x+17.065625=x[/tex]
[tex]x+4.03125x=17.065625[/tex]
[tex]5.03125x=17.065625[/tex]
[tex]x=\dfrac{17.065625}{5.03125}\approx3.392[/tex]
Put value of x in (2) , we get
[tex]y=\dfrac{3(3.392-5.3)}{-3.2}[/tex]
[tex]y=\dfrac{3(-1.908)}{-3.2}\approx1.789[/tex]
Hence, the intersection of the line through (0, 1) and (4.3, 2) and the line through (2.1, 3) and (5.3, 0) is (3.392, 1.789).
