Question

Find the intersection of the line through (0, 1) and (4.3, 2) and the line through (2.1, 3) and (5.3, 0).

Answer 1

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 :-

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

Similarly , the equation of line that passes through (0, 1) and (4.3, 2)  would  be:

$(y-1)=\dfrac{2-1}{4.3-0}(x-0)$

$(y-1)=\dfrac{1}{4.3-}(x)$

$4.3(y-1)=x$

$4.3y-4.3=x-----(1)$

Equation of line that passes through (2.1, 3) and (5.3, 0) would  be:

$(y-0)=\dfrac{3-0}{2.1-5.3}(x-5.3)$

$y=\dfrac{3(x-5.3)}{-3.2}-----(2)$

To find the intersection point (x,y) , we substitute the value of y from (2)in (1) , we get

$4.3(\dfrac{3(x-5.3)}{-3.2})-4.3=x$

$-4.03125(x-5.3)-4.3=x$

$-4.03125x+21.365625-4.3=x$

$-4.03125x+17.065625=x$

$x+4.03125x=17.065625$

$5.03125x=17.065625$

$x=\dfrac{17.065625}{5.03125}\approx3.392$

Put value of x in (2) , we get

$y=\dfrac{3(3.392-5.3)}{-3.2}$

$y=\dfrac{3(-1.908)}{-3.2}\approx1.789$

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).