Question

If P(4; 2) is the midpoint between A and B(6:3), determine he coordinates of A

Answer 1

$\large\sf\underline{Given:}$

• Midpoint P = ( 4 , 2 )

• Point B = ( 6 , 3 )

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$\large\sf\underline{To\:find:}$

• Coordinates of point A

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$\large\sf\underline{Solution:}$

Let the coordinates of A be ( x₁ , y₁ )

From the mid-point theorem ,

We know , mid-point ( x , y )

$\small{\underline{\boxed{\mathrm\purple{x=\frac{x₁+x₂}{2}\:\:and\:\:y=\frac{y₁+y₂}{2}}}}}$

Here ,

• x = 4⠀⠀‎⠀,⠀⠀‎ y = 2

• x₂ = 6⠀⠀‎ ,⠀⠀ y₂ = 3

Now substituting the value in our Formula :

$\sf➞\:x=\frac{x₁+x₂}{2}$

$\sf➞\:4=\frac{x₁+6}{2}$

• Cross multiplying

$\sf➞\:x₁+6=4×2$

$\sf➞\:x₁+6=8$

$\sf➞\:x₁=8-6$

$\small\fbox\pink{➞\:x₁=2}$

Similarly ,

$\sf➞\:y=\frac{y₁+y₂}{2}$

$\sf➞\:2=\frac{y₁+3}{2}$

• Cross multiplying

$\sf➞\:y₁+3=2×2$

$\sf➞\:y₁+3=4$

$\sf➞\:y₁=4-3$

$\small\fbox\pink{➞\:y₁=1}$

So the coordinates of A = ( x₁ , y₁ ) ${\sf{{\orange{=\:(2,1)}}}}$

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!! Hope it helps !!