Answer:
[tex]\left(-34, \dfrac{33}{2}\right)[/tex]
Step-by-step explanation:
Create a linear equation for line AB and line CD
Find slope using slope formula [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
then use point-slope form of linear equation [tex]y-y_1=m(x-x_1)[/tex]
(where m is the slope and [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two points on the line)
Line AB
[tex]m=\dfrac{-16+1}{-8+20}=-\dfrac54[/tex]
[tex]\implies y+1=-\dfrac54(x+20)\\\\\implies y=-\dfrac54x-26[/tex]
Line CD
[tex]m=\dfrac{0+11}{-19+9}=-\dfrac{11}{10}[/tex]
[tex]\implies y+11=-\dfrac{11}{10}(x+9)\\\\\implies y=-\dfrac{11}{10}x-\dfrac{209}{10}[/tex]
To find the point of intersection, equate the equations and solve for x::
AB = CD
[tex]\implies -\dfrac54x-26=-\dfrac{11}{10}x-\dfrac{209}{10}[/tex]
[tex]\implies -\dfrac{3}{20}x=\dfrac{51}{10}[/tex]
[tex]\implies x=-34[/tex]
Substitute found value of x into one of the equations and solve for y:
[tex]y=-\dfrac54(-34)-26=\dfrac{33}{2}[/tex]
Therefore, point of intersection is [tex]\left(-34, \dfrac{33}{2}\right)[/tex]
