Question

Find the mid-point of the segment joining the points P (6, 17) and Q (8, 15).​

Answer 1

Step-by-step explanation:

we know , midpoint=

√(x2-x1)²+(y2-y1)²

=√(8-6)²+(15-17)²

=√2²+2²

=2√2

Answer 2

Given

• A line segment is given with points P(6,17) and Q(8,15).

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To find

• Mid point of line segment PQ.

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Solution

• Let a point A(x,y) which divides the line segment PQ into two equal parts.

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★ A is the mid point of PQ.

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P(6,17)⠀⠀⠀⠀⠀⠀⠀⠀A(x,y)⠀⠀⠀⠀⠀⠀⠀⠀Q(8,15)

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⠀⠀⠀⠀⠀Using Formula

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$\: \: \: \: \boxed{\bf{\bigstar{A(x,y) = \bigg\lgroup{\dfrac{x_1 + x_2}{2},\dfrac{y_1 + y_2}{2}{\bigg\rgroup}}{\bigstar}}}}$

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Here,

• $\sf{x_1 = 6\: and\: x_2 = 8}$
• $\sf{y_1 = 17\: and\: y_2 = 15}$

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★ Putting the values

$\tt:\implies\: \: \: \: \: \: \: \: {A(x,y) = \bigg\lgroup{\dfrac{6 + 8}{2},\dfrac{17 + 15}{2}{\bigg\rgroup}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {A(x,y) = \bigg\lgroup{\dfrac{14}{2},\dfrac{32}{2}{\bigg\rgroup}}}$

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$\bf:\implies\: \: \: \: \: \: \: \: {A(x,y) = \bigg\lgroup{7,16{\bigg\rgroup}}}$

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Hence,

• The midpoint of the line segment PQ is A(7,16).

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