Question
Mathematics
Decide whether the lines given are parallel, perpendicular, or neither.
The line through $\left(-10,4\right)$(-10,4) and $\left(8,9\right)$(8,9).
The line through $\left(4,-4\right)$(4,-4) and $\left(-14,1\right)$(-14,1).
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To determine if the two lines are parallel, perpendicular, or neither, we need to find the slopes of the two lines.
The slope of the first line through $\left(-10,4\right)$(-10,4) and $\left(8,9\right)$(8,9) is:
${m}_{1}=\frac{9-4}{8-\left(-10\right)}=\frac{5}{18}$m_(1)=(9-4)/(8-(-10))=(5)/(18)
The slope of the second line through $\left(4,-4\right)$(4,-4) and $\left(-14,1\right)$(-14,1) is:
${m}_{2}=\frac{1-\left(-4\right)}{-14-4}=-\frac{5}{18}$m_(2)=(1-(-4))/(-14-4)=-(5)/(18)
Since the product of the slopes is:
${m}_{1}\cdot {m}_{2}=\frac{5}{18}\cdot \left(-\frac{5}{18}\right)=-\frac{25}{324}$m_(1)*m_(2)=(5)/(18)*(-(5)/(18))=-(25)/(324)
which is not equal to $1$1, the two lines are not perpendicular.
Furthermore, the slopes are negative reciprocals of each other, which tells us that the two lines are perpendicular if the sign of one of the slopes is flipped. Since neither slope needs to be flipped, the two lines are not perpendicular either.
Therefore, the two lines are neither parallel nor perpendicular.
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