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Question

Find the coordinates of the midpoint of the line joining the points $$(-3, 10)$$ and $$(6, -8)$$.


Solution

We know that the mid point formula $$M=(x,y)$$ of the two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ is:

$$(x,y)=\left( \dfrac { { x }_{ 1 }{ +x }_{ 2 } }{ 2 } ,\dfrac { { y }_{ 1 }{ +y }_{ 2 } }{ 2 }  \right)$$  

Here, the given points are $$(-3,10)$$ and $$(6,-8)$$, therefore,

$$(x,y)=\left( \dfrac { { x }_{ 1 }{ +x }_{ 2 } }{ 2 } ,\dfrac { { y }_{ 1 }{ +y }_{ 2 } }{ 2 }  \right) \\ \Rightarrow (x,y)=\left( \dfrac { -3+6 }{ 2 } ,\dfrac { 10+(-8) }{ 2 }  \right) \\ \Rightarrow (x,y)=\left( \dfrac { 3 }{ 2 } ,\dfrac { 10-8 }{ 2 }  \right) \\ \Rightarrow (x,y)=\left( \dfrac { 3 }{ 2 } ,\dfrac { 2 }{ 2 }  \right) \\ \Rightarrow (x,y)=\left( \dfrac { 3 }{ 2 } ,1 \right)$$  
 
Hence, the coordinates of the mid point are $$\left( \dfrac { 3 }{ 2 } ,1 \right)$$.

Mathematics

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