For the point P(25,13) and Q(30,16), find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ

The formula of the distance between two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
The mid-point of a line whose end points are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

∵ Point P = (25 , 13)

∵ Point Q = (30 , 16)

- Use the formula of the distance to find [tex]d_{PQ}[/tex]

∴ [tex]x_{1}[/tex] = 25 and [tex]x_{2}[/tex] = 30

∴ [tex]y_{1}[/tex] = 13 and [tex]y_{2}[/tex] = 16

- Substitute these values in the formula above

∵ [tex]d_{PQ}=\sqrt{(30-25)^{2}+(16-13)^{2}}=\sqrt{(5)^{2}+(3)^{2}}[/tex]

∴ [tex]d_{PQ}=\sqrt{25+9}=\sqrt{34}[/tex]

∴ [tex]d_{PQ}[/tex] = 5.83 units

The distance of PQ is 5.83 units

Let us find the mid-point M of segment PQ

∵ M = [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

∵ [tex]x_{1}[/tex] = 25 and [tex]x_{2}[/tex] = 30

∵ [tex]y_{1}[/tex] = 13 and [tex]y_{2}[/tex] = 16

- Substitute these values in the rule of mid-point above

∴ [tex]M=(\frac{25+30}{2},\frac{13+16}{2})[/tex]

∴ [tex]M=(\frac{55}{2},\frac{29}{2})[/tex]

∴ M = (27.5 , 14.5)

The midpoint M of the segment PQ is (27.5 , 14.5)

Learn more:

You can learn more about the mid-point in brainly.com/question/5223123

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