Answer:
M(x₄ ,y₄) = (-3.5 , 0.5) and
N (x₅ ,y₅) = ( -1 , -0.5 )
Step-by-step explanation:
Let the endpoint coordinates for the mid segment of △PQR that is parallel to PQ be
M(x₄ ,y₄) and N(x₅ ,y₅) such that MN || PQ
point P( x₁ , y₁) ≡ ( -3 ,3 )
point Q( x₂ , y₂) ≡ (2 , 1 )
point R( x₂ , y₂) ≡ (-4 , -2)
To Find:
M(x₄ ,y₄) = ? and
N (x₅ ,y₅) = ?
Solution:
We have Mid Point Formula as
[tex]Mid\ point(x,y)=(\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2})[/tex]
As M is the mid point of PR and N is the mid point of RQ so we will have
[tex]Mid\ pointM(x_{4} ,y_{4})=(\frac{x_{1}+x_{3} }{2}, \frac{y_{1}+y_{3} }{2})[/tex]
[tex]Mid\ pointN(x_{5} ,y_{5})=(\frac{x_{2}+x_{3} }{2}, \frac{y_{2}+y_{3} }{2})[/tex]
Substituting the given value in above equation we get
[tex]Mid\ pointM(x_{4} ,y_{4})=(\frac{-3+-4 }{2}, \frac{3+-2} }{2})[/tex]
∴ [tex]Mid\ pointM(x_{4} ,y_{4})=(\frac{-7} }{2}, \frac{1}{2})[/tex]
∴ [tex]Mid\ pointM(x_{4} ,y_{4})=(-3.5, 0.5)[/tex]
Similarly,
[tex]Mid\ pointN(x_{5} ,y_{5})=(\frac{2+-4 }{2}, \frac{1+-2 }{2})[/tex]
∴ [tex]Mid\ pointN(x_{5} ,y_{5})=(\frac{-2 }{2}, \frac{-1}{2})[/tex]
∴ [tex]Mid\ pointN(x_{5} ,y_{5})=(-1, -0.5)[/tex]
∴ M(x₄ ,y₄) = (-3.5 , 0.5) and
N (x₅ ,y₅) = ( -1 , -0.5 )
