Product of slopes of two perpendicular lines= -1

True

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False

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Solution

The correct option is A
True

If $m_{1}$ and $m_{2}$ be the slopes of two lines, $θ$ be the angle between them

$t a n θ = ∣ ∣ \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} ∣ ∣$

If $θ = 90^{\circ}$

$t a n 90^{\circ} = ∣ ∣ \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} ∣ ∣$

Then $θ = 90^{\circ} t a n θ$ is not defined

Denominator = $1 + m_{1} . m_{2} = 0$

$m_{1} . m_{2} = - 1$

So, gives statement is true.

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Similar questions

Statement 1 : If two lines are perpendicular, then product of their slopes is –1.
Statement 2: If the product of slopes of two lines is –1, then these lines will be perpendicular.

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Product of slopes of two perpendicular lines= -1

The correct option is A True If m1 and m2 be the slopes of two lines, θ be the angle between them tanθ=∣∣m1−m21+m1m2∣∣ If θ=90∘ tan90∘=∣∣m1−m21+m1m2∣∣ Then θ=90∘tanθ is not defined Denominator = 1+m1.m2=0 m1.m2=−1 So, gives statement is true.