climmilk
Answered

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

Sagot :

r3t40

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

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

[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]

The first slope of a line passing through [tex]PQ[/tex] is

[tex]m_1=\frac{-13-(-9)}{6-2}=\frac{-4}{4}=-1[/tex]

The second slope of a line passing through [tex]RS[/tex] is

[tex]m_2=\frac{-1-(-5)}{5-1}=\frac{4}{4}=1[/tex]

Now check if [tex]m_1=-\frac{1}{m_2}[/tex] is true

[tex]-1=-\frac{1}{1}\implies -1=-1[/tex]

This means the two lines are perpendicular.

Hope this helps.

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