Answer:
[tex]A'(2,\frac{31}{5})[/tex]
Step-by-step explanation:
Remember that three points are collinears if they stay in the same line.
To find the line that pass through A(-2,3) and A''(3,7), we find first the slope of the line and then the y-intercept.
The slope of the line is
[tex]m=\frac{7-3}{3-(-2)}=\frac{4}{5}[/tex]
The y-intercept of the line is
[tex]7=\frac{4}{5}*3+b\\b=\frac{23}{5}[/tex]
Then the equation of the line is
[tex]y=\frac{4}{5}x+\frac{23}{5}[/tex]
Since we want that the point A'(x,y) stay in the line, then we need to choose a value for x and replace in the equation found.
If we take x=2
[tex]y=\frac{4}{5}*2+\frac{23}{5}=\frac{31}{5}[/tex]
Then the points [tex]A(-2,3), A'(2, \frac{31}{5}), A''(3,7)[/tex] are collinear.
