Question

If the midpoint of segment AB is M(1,-3) and B(5,-10), find the coordinates of point A.

Answer 1

Answer:

Therefore the required point A(x₁ , y₁)  = A( -3 , 4 )

Step-by-step explanation:

Given:

The midpoint of segment AB is M(1,-3)

and B(5,-10),

Let

point A( x₁ , y₁)  

point B( x₂ , y₂) ≡ (5 , -10)

M(x , y) = (1 , -3 )

To Find:

point A( x₁ , y₁)  = ?

Solution:

M is the midpoint of segment AB.    {Given}

BY Mid point Formula we have

$M(x,y)=(\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2})$

Substituting the given values in above equation we get

$M( 1, -3)=(\frac{x_{1}+5 }{2}, \frac{y_{1}-10 }{2})\\\\\textrm{on equating the X coordinate and Y coordinate of M we get}\\1 =\frac{x_{1}+5 }{2}\\\\and\\-3=\frac{y_{1}-10 }{2}\\\\\therefore x_{1}+5=2\ and\ y_{1}-10 =-6\\\\\therefore x_{1} = 2-5=-3\ and\ y_{1}=10-6=4\\\\\therefore x_{1} = -3\ and \ y_{1}=4\\\\\therefore A(x_{1},y_{1})=A(-3,4)$

Therefore the required point A(x₁ , y₁)  = A( -3 , 4 )