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KAntoineDoixidn

✒️DISTANCE/MIDPOINT

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[tex] \large\underline{\mathbb{ANSWER}:} [/tex]

[tex] \qquad \Large \: \rm Distance:\; 13 \: units [/tex]

[tex] \qquad \Large \:\rm Midpoint: \; (8, \,5.5) [/tex]

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[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]

Determine the distance between the given points using the distance formula.

[tex] \begin{align} & \bold{Formula:} \\ & \quad \boxed{\rm d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2\,}} \end{align} [/tex]

  • [tex] d = \sqrt{(14-2)^2 + (8-3)^2\,} [/tex]

  • [tex] d = \sqrt{(12)^2 + (5)^2\,} [/tex]

  • [tex] d = \sqrt{144 + 25\,} [/tex]

  • [tex] d = \sqrt{169\,} [/tex]

  • [tex] d = 13 [/tex]

Therefore, the distance between points P and Q is 13 units.

Find the Midpoint of the segment PQ using the midpoint formula.

[tex] \begin{align} & \bold{Formula:} \\ & \quad \boxed{\rm Midpoint = \bigg(\frac{x_1+x_2}2,\,\frac{y_1+y_2}2\bigg)} \end{align} [/tex]

  • [tex] \rm Midpoint = \bigg(\frac{2+14}2,\,\frac{3+8}2\bigg) \\ [/tex]

  • [tex] \rm Midpoint = \bigg(\frac{16}2,\,\frac{11}2\bigg) \\ [/tex]

  • [tex] \rm Midpoint = (8,\,5.5) \\ [/tex]

Therefore, the coordinates of the midpoint between the segment PQ is (8, 5.5)

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