Question

Let A (6,4) and B(2,12) , find the slope of a line perpendicular to AB.​

Answer 1

Given A(6,4),B(2,12)

Let m be the slope of AB. Then,

we know that slope of line passing through (x

1

,y

2

),(x

2

,y

2

)=

x

2

−x

1

y

2

−y

1

m=

2−6

12−4

=

−4

8

=−2

slope of two perpendicular lines m

1

m

2

=−1⇒m

2

=

m

1

−1

So, the slope of a line perpendicular to AB is − m 1 = 2 / 1

.

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Answer 2

Solution :

If we're having with (x1 , y1) and (x2 , y2) are co-ordinates of two points then it's slope (m) is calculated by the formula :

• $\red{\boxed{\bf{m \: = \: \dfrac{ y_{2} \: - \:y_{1}}{ x_{2} \: - \:x_{1} } }}}$

Given :

• x1 = 6
• y1 = 4
• x2 = 2
• y2 = 12

Applying the values in the formula :

$\implies\sf{m \: = \: \dfrac{ y_{2} \: - \:y_{1}}{ x_{2} \: - \:x_{1} } } \\ \\ \implies\sf{m \: = \: \dfrac{12 - 4}{ 2 - 6} } \\ \\ \implies\sf{m \: = \: \dfrac{8}{ - 4} } \\ \\ \implies\sf{m \: = \: - \dfrac{8}{ 4} } \\ \\ \implies\sf{m \: = \: - \cancel{\dfrac{8}{4} }} \\ \\ \implies \: \red{\bf{m \: = \: - 2 }}$

As we know if two slopes are perpendicular then product of their slopes is -1.

• $\boxed{ \pink{\bf{m_{1} \: . \: m _{2} \: = \: - 1}}}$

$\longmapsto \: \sf{ - 2 \: . \:m_{2} = - 1} \\ \\ \longmapsto \: \sf{ m_{2} = \frac{ - 1}{ - 2} } \\ \\ \longmapsto \: \bf{ m_{2} = \: \dfrac{ 1}{ 2} }$