Answer:
No, it does not pass through point C.
Step-by-step explanation:
We are given two points on a line:
- [tex]A\ (-3, -2)[/tex]
- [tex]B\ (2, 1)[/tex]
and we are asked whether or not the point:
is also on the line.
First, we can create an equation in point-slope form for the line.
Its slope can be determined using the equation:
[tex]m = \dfrac{\text{rise}}{\text{run}} = \dfrac{\Delta y}{\Delta x}[/tex]
[tex]m= \dfrac{1-(-2)}{2-(-3)}[/tex]
[tex]m=\dfrac{3}{5}[/tex]
Point-slope form is given by:
[tex]y-b=m(x-a)[/tex]
where [tex](a,b)[/tex] is a point on the line and [tex]m[/tex] is its slope.
Plugging in the known variables, we get:
- [tex]m=3/5[/tex]
- [tex]a=2[/tex]
- [tex]b=1[/tex]
↓↓↓
[tex]y-1=\dfrac{3}{5}(x-2)[/tex]
Then, we can check if point C is on the line by substituting its x- and y-coordinates in for those variables in the point-slope equation:
- [tex]x=5[/tex]
- [tex]y=3[/tex]
↓↓↓
[tex]3-1\stackrel{?}{=}\dfrac{3}{5}(5-2)[/tex]
[tex]2\stackrel{?}{=}\dfrac{3}{5}(3)[/tex]
[tex]2 \ne \dfrac{9}{5}[/tex]
Since the resulting equation is not true, point C is NOT on the line that passes through points A and B.
Further Note
The fact that [tex]2[/tex] and [tex]9/5[/tex] are almost equal tells us that the point is close to the line, but not on it.
