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Answer:
The missing coordinate [tex]r[/tex] is 9.
Step-by-step explanation:
Given the points [tex]P(x,y) = (-3,-3)[/tex] and [tex]Q(x,y) = (5,r)[/tex], the slope of a line passing the two points ([tex]m_{PQ}[/tex]) is determined by equation of secant line:
[tex]m_{PQ} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}[/tex] (1)
[tex]m_{PQ} = \frac{r-(-3)}{5-(-3)}[/tex]
If we know that [tex]m_{PQ} = \frac{3}{2}[/tex], then the value of [tex]r[/tex] is:
[tex]\frac{3}{2} = \frac{r+3}{8}[/tex]
[tex]12 = r + 3[/tex]
[tex]r = 9[/tex]
The missing coordinate [tex]r[/tex] is 9.