Climmilkidn
Answered

Dive into the world of knowledge and get your queries resolved at IDNLearn.com. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.

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 :

R3t40idn

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.

We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com is your go-to source for accurate answers. Thanks for stopping by, and come back for more helpful information.