AIR MATH

Math Question

In this coordinate plane, line \( a \) is perpendicular to line \( b \).
Complete the proof that the slope of \( a \) is equal to the opposite reciprocal of the slope of \( b \).
Line \( a \) is perpendicular to line \( b \), which means \( = \) is a right angle. So, \( = \) is
a right triangle. The altitude \( I N \) to the hypotenuse in the right triangle \( \triangle K M L \) creates two
similar right triangles, which means \( - \). Since corresponding sides of similar
triangles are proportional, \( = \) Further, since \( L N=n, M N=m \), and \( K N=k_{t} \)
- by substitution.
The slope of a line is defined as the change in \( y \) divided by the change in \( x \). Two points on
line \( a \) are \( L(0,0) \) and \( M(m, n) . \) So, the slope of line \( a \) is
- Two points on line \( b \) are \( L \)
\( (0,0) \) and \( K(-k, n) . \) So, the slope of line \( b \) is
- This means the opposite reciprocal of
the slope of \( b \) is \( - \) Therefore, the slope of \( a \) is equal to the opposite reciprocal of the
slope of \( b \).

Solution

solution

AIR MATH homework app,
absolutely FOR FREE!

  • AI solution in just 3 seconds!
  • Free live tutor Q&As, 24/7
  • Word problems are also welcome!
appstoreplaystore

Scan the QR code below
to download AIR MATH!

qrcode