Question

True or False? In Exercises 99 and 100, determine whether the statement is true or false. Justify your answer, : 99. The line through (−8,2) and (−1,4) and the line through (0,−4) and (−7,7) are parallel.

Alternate coordinate systems
ANSWERED
asked 2020-11-22
True or False? In Exercises 99 and 100, determine whether the statement is true or false. Justify your answer, : 99. The line through (−8,2) and (−1,4) and the line through (0,−4) and (−7,7) are parallel.

Answers (1)

2020-11-23
The given statement is False.
Reason: The slope of the line passing through the points (x1,y1) and (x2,y2) is given by
\(\displaystyle{m}=\frac{{{y}{1}-{y}{2}}}{{{x}{1}-{x}{2}}}\)
Using this formula the slope of the line through (−8,2) and (−1,4) is given by
\(\displaystyle{m}{1}=\frac{{{2}-{4}}}{{-{8}+{1}}}=\frac{{2}}{{7}}\)
And the slope of the line through (0,−4) and (−7,7) is
\(\displaystyle{m}{2}=\frac{{-{4}-{7}}}{{{0}+{7}}}=-{\left(\frac{{11}}{{7}}\right)}\)
Since, the slopes m1 and m2 are not equal or not proportional, the given lines are not parallel.
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