Answer:
C) They are perpendicular lines.
Step-by-step explanation:
We first need to find the slope of the graph of the lines passing through these points using:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
The slope of the line that passes through (−12, 15) and (4, −5) is
[tex] m_{1} = \frac{ - 5 - 15}{4 - - 12} [/tex]
[tex]m_{1} = \frac{ - 20}{16} = - \frac{5}{4} [/tex]
The slope of the line going through (−8, −9) and (16, 21) is
[tex] m_{2} = \frac{21 - - 9}{16 - - 8} [/tex]
[tex] m_{2} = \frac{21 + 9}{16 + 8} [/tex]
[tex]m_{2} = \frac{30}{24} = \frac{5}{4} [/tex]
The product of the two slopes is
[tex]m_{1} \times m_{2} = - \frac{4}{5} \times \frac{5}{4} = - 1[/tex]
Since
[tex]m_{1} \times m_{2} = - 1[/tex]
the two lines are perpendicular.
