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Step 1:I'll solve this step by step, following the LaTeX formatting guidelines precisely.
Problem 7: $(-1,-11)$ and $(-6,-7)$
Slope Calculation Formula:
Step 2:: Identify coordinates
- $$x_{1} = -1, y_{1} = -11
- x_{2} = - 6, y_{2} = - 7
Step 3:: Calculate slope
Problem 8: $(-7,-13)$ and $(1,-5)$
Step 4:: Identify coordinates
- $$x_{1} = -7, y_{1} = -13
- x_{2} = 1, y_{2} = - 5
Step 5:: Calculate slope
Problem 9: $(8,3)$ and $(-5,3)$
Step 6:: Identify coordinates
- $$x_{1} = 8, y_{1} = 3
- x_{2} = - 5, y_{2} = 3
Step 7:: Calculate slope
Problem 10: $(15,7)$ and $(3,-2)$
Step 8:: Identify coordinates
- $$x_{1} = 15, y_{1} = 7
- x_{2} = 3, y_{2} = - 2
Step 9:: Calculate slope
Problem 11: $(-5,-1)$ and $(-5,-10)$
Step 10:: Identify coordinates
- $$x_{1} = -5, y_{1} = -1
- x_{2} = - 5, y_{2} = - 10
Step 11:: Calculate slope
Problem 12: $(-12,16)$ and $(-4,-2)$
UNDEFINED (vertical line)
Step 12:: Identify coordinates
- $$x_{1} = -12, y_{1} = 16
- x_{2} = - 4, y_{2} = - 2
Step 13:: Calculate slope
m = \frac{-2 - 16}{-4 - (-12)} = \frac{-18}{8} = -\frac{9}{4}
Problem 13: Parallel/Perpendicular Lines
Step 14:: Calculate slope of PQ
- $$P(9,-4), Q(-7,-1)
m_{PQ} = \frac{- 1 - (- 4)}{- 7 - 9} = \frac{3}{- 16} = -\frac{3}{16}
Step 15:: Calculate slope of RS
- $$R(-2,5), S(-6,-1)
m_{RS} = \frac{- 1 - 5}{- 6 - (- 2)} = \frac{- 6}{- 4} = \frac{3}{2}
Step 16:: Determine line relationship
Since $$m_{PQ} = -\frac{3}{16} \neq m_{RS} = \frac{3}{2}$$, the lines are NEITHER parallel nor perpendicular.
- Parallel lines have equal slopes - Perpendicular lines have negative reciprocal slopes
Final Answer
7. -\frac{4}{5} 8. 1 9. 0 10. \frac{3}{4} 11. Undefined 12. -\frac{9}{4} 13. Neither parallel nor perpendicular
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