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Kazeer [188]
2 years ago
13

Is the line through points P(2,-9) and Q(6, -13) perpendicular to the line through points R(5,-1) and

Mathematics
1 answer:
ruslelena [56]2 years ago
6 0

Two lines y_1,y_2 are perpendicular if their slopes are in a relation m_1=-\frac{1}{m_2}.

So we need to find slopes and if the above relation holds then we can claim the lines are perpendicular.

To find slopes, use slope formula

m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}

The first slope of a line passing through PQ is

m_1=\frac{-13-(-9)}{6-2}=\frac{-4}{4}=-1

The second slope of a line passing through RS is

m_2=\frac{-1-(-5)}{5-1}=\frac{4}{4}=1

Now check if m_1=-\frac{1}{m_2} is true

-1=-\frac{1}{1}\implies -1=-1

This means the two lines <em>are</em> perpendicular.

Hope this helps.

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