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Sagot :
SOLUTION
Write out the given coordinate of point P and Q
[tex]\begin{gathered} P=(-3,0) \\ \text{and} \\ Q=(4,3) \end{gathered}[/tex]
The distance between two point is given by
[tex]\text{dist}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}^{}[/tex]
Given point P(-3,0) and Q(4,3)
[tex]\begin{gathered} x_2=4,x_1=-3,y_2=3,y_1=0 \\ \text{Then } \\ \text{dist(P,Q)}=\sqrt[]{(4-(-3)^2+(3-0)^2} \end{gathered}[/tex]Hence, by simplification, we have
[tex]\begin{gathered} \text{dist(P,Q)}=\sqrt[]{7^2+3^2}=\sqrt[]{49+9}=\sqrt[]{58} \\ \end{gathered}[/tex]Hence
The distance between point P and Q is √58 unit
Then
The coordinates of the midpoint is given by
[tex]\begin{gathered} Let\text{ the coordinate of the midpoint m be } \\ (x_m,y_m) \\ \text{Hence } \\ (x_m,y_m)=(\frac{x_1+x_2}{2}+\frac{y_1+y_2}{2}) \end{gathered}[/tex]
Where
[tex]\begin{gathered} x_2=4,x_1=-3,y_2=3,y_1=0 \\ \text{Then} \\ (x_m,y_m)=(\frac{-3+4}{2},\frac{3+0}{2}) \\ \\ (x_m,y_m)=(\frac{1}{2},\frac{3}{2}) \end{gathered}[/tex]Therefore
The coordinates of the midpoint M of the segment PQ is (1/2,3/2)
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