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alisha [4.7K]
2 years ago
8

2x-5y=-3 5x+2y=6 Is this a perpendicular lines ?

Mathematics
1 answer:
creativ13 [48]2 years ago
4 0

Perpendiculat Line is when both slopes of equation multiplying each others and equal to -1.

\large \boxed{m_1m_2 =   - 1}

For an easier way to understand, a perpendicular line has a negative reciprocal slope. For example if we are given the equation of y = 2x then the equation that is perpendicular to y = 2x would be y = (-1/2)x.

From both equations. We can either arrange in slope-intercepy form or use the slope formula which is m = -A/B when the equation is in Ax+By+C = 0 or Ax+By = C.

\large{ \begin{cases} 2x - 5y =  - 3 \\  5x + 2y = 6 \end{cases}}

To find if these two lines are perpendicular to each others. Use the slope formula of -A/B.

\large{ \begin{cases} m_1 =  -  \frac{2}{ - 5}  \\ m_2 =  -  \frac{5}{2}  \end{cases}} \\  \large{ \begin{cases} m_1 =   \frac{2}{ 5}  \\ m_2 =  -  \frac{5}{2}  \end{cases}}

Now recall that it is perpendicular when one of them is negative reciprocal of one another (-5/2 is negative reciprocal of -(-2/5) = 2/5 and 2/5 is negative reciprocal of -5/2).

Or in definition of perpendicular lines, both slopes multiply and must equal to -1.

\large{( \frac{2}{5} )( -  \frac{5}{2} ) =  - 1} \\  \large{ - 1 =  - 1}

Thus the equation is true which makes both lines perpendicular to each others.

Answer

  • Both lines are perpendicular to each others.

Let me know if you have any doubts!

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