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 \( b \).

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