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
[tex]M(x,y)=(\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2})[/tex]
Substituting the given values in above equation we get
[tex]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)[/tex]
Therefore the required point A(x₁ , y₁) = A( -3 , 4 )
