Question

What are the endpoint coordinates for the midsegment of △PQR that is parallel to PQ¯¯¯¯¯?

Answer 1

M(x₄ ,y₄) = (-3.5 , 0.5) and

N (x₅ ,y₅) = ( -1 , -0.5 )

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

`Mid\ point(x,y)=((x_(1)+x_(2) )/(2), (y_(1)+y_(2) )/(2))`

As M is the mid point of PR and N is the mid point of RQ so we will have

`Mid\ pointM(x_(4) ,y_(4))=((x_(1)+x_(3) )/(2), (y_(1)+y_(3) )/(2))`

`Mid\ pointN(x_(5) ,y_(5))=((x_(2)+x_(3) )/(2), (y_(2)+y_(3) )/(2))`

Substituting the given value in above equation we get

`Mid\ pointM(x_(4) ,y_(4))=((-3+-4 )/(2), \frac{3+-2} }{2})`

∴
`Mid\ pointM(x_(4) ,y_(4))=(\frac{-7} }{2}, (1)/(2))`

∴
`Mid\ pointM(x_(4) ,y_(4))=(-3.5, 0.5)`

Similarly,

`Mid\ pointN(x_(5) ,y_(5))=((2+-4 )/(2), (1+-2 )/(2))`

∴
`Mid\ pointN(x_(5) ,y_(5))=((-2 )/(2), (-1)/(2))`

∴
`Mid\ pointN(x_(5) ,y_(5))=(-1, -0.5)`

∴ M(x₄ ,y₄) = (-3.5 , 0.5) and

N (x₅ ,y₅) = ( -1 , -0.5 )