The legs of a right-angle triangle are perpendicular.
The slope of line ST must be -1/3
From the question, we have:
[tex]\mathbf{m_{RS} = 3}[/tex] --- the slope of RS
Because line ST is the other leg of the right-angle triangle, then the slope of line ST is:
[tex]\mathbf{m_{ST} = -\frac 1{m_{RS}}}[/tex]
Substitute [tex]\mathbf{m_{RS} = 3}[/tex]
[tex]\mathbf{m_{ST} = -\frac 13}[/tex]
Hence, the slope of line ST must be -1/3
Read more about slopes of perpendicular lines at:
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