Right Angle

If the graphs of the equations 3x-5y+4=0 and 2x+ay-11=0 intersect at right angles, find the value of a.
Source: NCTM Math Teacher 2008

SOLUTION
3x-5y+4=0
5y=3x+4
y=\dfrac{3}{5}x+\dfrac{4}{5}

2x+ay-11=0
ay=-2x+11
y=-\dfrac{2}{a}x+\dfrac{11}{a}
If the two graphs intersect at right angle, their slopes are negative reciprocal of each other
-\dfrac{2}{a}=-1\div\dfrac{3}{5}
\dfrac{2}{a}=\dfrac{5}{3}
Cross multiply
5a=6
a=\dfrac{6}{5}
Their graphs are shown below

Answer: \dfrac{6}{5}

Advertisements

About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s