Weber West
08/07/2023 · Senior High School
c) If the gradient of a line, \( C \). is \( \frac{2}{3} \), what is the gradient of the line which is perpendicular to \( C \) ?
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Step-by-step Solution
The gradient (or slope) of a line that is perpendicular to another line can be found using the negative reciprocal of the original line's gradient.
If the gradient of line \( C \) is \( \frac{2}{3} \), the gradient of the line that is perpendicular to \( C \) is calculated as follows:
1. Take the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \).
2. Change the sign to get the negative reciprocal:
\[
-\frac{3}{2}
\]
Therefore, the gradient of the line that is perpendicular to line \( C \) is \( -\frac{3}{2} \).
Quick Answer
The gradient of the perpendicular line is \( -\frac{3}{2} \).
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