Question

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A line is joining two points A(6,2) and B(2,8).
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Find :-
(i) Its midpoint
(ii) Its slope
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Answer 1

Given:

• AB is a line with points A(6,2) and B(2,8).

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To find:

1. Mid-point
2. Slope

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Solution:

• We have two coordinates of the line.
• Let the mid point of the line be P(x,y)

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➛ For finding the mid point, we use the given formula

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$\bf{\dag{P(x,y) = \bigg( \dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2} \bigg)}}$

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• Substituting the values

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$\tt{\longrightarrow{P(x,y) = \bigg( \dfrac{6 + 2}{2} , \dfrac{2 + 8}{2} \bigg)}}$

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$\tt{\longrightarrow{P(x,y) = \bigg( \dfrac{8}{2} , \dfrac{10}{2} \bigg)}}$

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$\tt{\longrightarrow{P(x,y) = (4 , 5)}}$

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Hence,

• Mid point of the given line is P(4 ,5)

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➛ Now, we will find the slope of tge line by using the given formula

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$\bf{\dag{Slope\: (m) = \bigg( \dfrac{y_2 - y_1}{x_2 - x_1} \bigg)}}$

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• Substituting the values

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$\tt{\longrightarrow{m = \bigg( \dfrac{8 - 2}{2 - 6} \bigg)}}$

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$\tt{\longrightarrow{m = \dfrac{6}{-4}}}$

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$\tt{\longrightarrow{m = - \dfrac{3}{2}}}$

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Hence,

• Slope of the given line is $\rm{- \dfrac{3}{2}}$.

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Answer 2

Solution

Given :-

• Joining Point of a line is A(6,2) & B(2,8)

Find :-

• It's Midpoint
• It's Slope

Explanation

Let,

If any two point are P(x' , y') & Q(x" , y").

Then , Midpoint will. be of these point

$\dag\boxed{\underline{\tt{\red{\:Midpoint\:=\:\big(\dfrac{x'+x"}{2}\:,\dfrac{y'+y"}{2}\big)}}}}$

$\dag\boxed{\underline{\tt{\orange{\:Slope\:=\:\dfrac{y"-y'}{x"-x'}}}}}$

Here,

• x' = 6 , x" = 2
• y' = 2 , y" = 8

First Calculate Midpoint,

==> Midpoint of these two point = (( 6+2)/2 , (2+8)/2)

==> Midpoint of these two point = (8/2 , 10/2)

==> Midpoint of these two point = (4, 5)

Now, Calculate Slope,

==> Slope of line = (8-2)/(2-6)

==> Slope of line = 6/(-4)

==> Slope of line = -3/2

Here, Slope is Negative ,

That's means a line is trending downward from left to right.

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