Question

Find the midpoint of the line segment with end coordinates of: (−3,−1) and (4,−5) Give coordinates as decimals where appropriate.
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Question for 50pts so don't spam mate✌✌​

Answer 1

DIAGRAM:-

A ∘──────────∘───────────∘ B

(-3,-1)⠀⠀⠀⠀⠀⠀ ⠀⠀ C⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ (4,-5)

Given:-

• Coordinates of Point A = ( - 3, -1)

• Coordinates of Point B = (4, -5)

To find:-

• Midpoint of the line segment ( C ) = ?

Solution:-

$\sf x_1 = -3$

$\sf x_2 = 4$

$\sf y_1 = -1$

$\sf y_2 = -5$

$\star\;{\boxed{\sf{\pink{Midpoint\;formula = \dfrac{ x_1 + x_2 }{2} \;and\; \dfrac{ y_1 + y_2 }{2} }}}}$

$\sf\underline{\bigstar\;Putting\;values\;:}$

$\bullet\;\;\sf \dfrac{ x_1 + x_2 }{2} \\ \\ :\implies\sf \dfrac{-3 + 4}{2} \\ \\ :\implies\sf \dfrac{1}{2} \\ \\ :\implies\bf {\underline{\boxed{\bf{\purple{0.5}}}}} \\ \\ \bullet\;\;\sf \dfrac{ y_1 + y_2 }{2} \\ \\ :\implies\sf \dfrac{-1 + (-5)}{2} \\ \\ :\implies\sf \dfrac{-6}{2} \\ \\ :\implies\bf {\underline{\boxed{\bf{\purple{-3}}}}}$

$\therefore\;{\underline{\sf{Hence,\;the\;mid\;point\;of\; C\;is\;\bf{0.5\;and\;-3}.}}}$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀

Answer 2

Mid-point of a line segment

Given:

Coordinates of one end of line segment $=(-3,-1)$ let say Point A

Coordinates of other end of line segment $=(4,-5)$  let say Point B

To find:

Coordinates of mid-point, let say Point C

Explanation:

Formula of mid point for x coordinates = $\frac{x_{1}+x_{2} }2$

Formula of mid point for x coordinates = $\frac{y_{1}+y_{2} }2$

Hence coordinates of mid points are  $[\frac{x_{1}+x_{2} }2,\frac{y_{1}+y_{2} }2]$

Here,

$x_{1}=-3$  

$x_{2}=4\\y_{1}=-1\\y_{1}=-5$

On putting values in mid point formula we get,

x coordinates of C as $0.5$

y coordinates of C as $-3$

So, coordinates of Point C ( mid-point of line segment AB) = $(0.5,-3)$.