Question

Find the mid-point of the line joining the points (3, 0) and (–1, 4).

Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

• Find the mid-point of the line joining the points (3, 0) and (–1, 4)

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♣ ᴀɴꜱᴡᴇʀ :

$\huge\boxed{\sf{Midpoint=1,2}}$

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♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

Let the line segment have vertices A and B

$\setlength{\unitlength}{1cm}\begin{picture}(6,6)\put(1.85,3.9){\textbullet}\put(2, 4){\line(1, 0){6}} \put(1.8,3.5){\sf A}\put(2.7,4.5){\sf }}\put(4.8,4.5){\sf }\put(6.8,4.5){\sf }\put(7.9,3.5){\sf B}\put(7.9,3.9){\textbullet}\end{picture}$

Then given points :

A (3, 0) and B (–1, 4)

We are asked to find midpoint of line segment AB

Midpoint formula is given by :

$\boxed{\sf{Midpoint=\dfrac{x_1+x_2}{2},\:\dfrac{y_1+y_2}{2}}}$

In the given points :

x₁ = 3

x₂ = -1

y₁ = 0

y₂ = 4

Now substituting the values into the formula :

$\sf{Midpoint=\dfrac{3+(-1)}{2},\:\dfrac{0+4}{2}}$

$\sf{Midpoint=\dfrac{3-1}{2},\:\dfrac{4}{2}}$

$\sf{Midpoint=\dfrac{2}{2},\:\dfrac{4}{2}}$

$\huge\boxed{\sf{Midpoint=1,2}}$