DISTANCE
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[tex]\large\sf\underline{Problem:} [/tex]
- determine the distance between P and Q.
- P(3,5) Q(3,-2)
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[tex]\large\sf\underline{Answer:}[/tex]
[tex] \qquad \huge \rm PQ = 7\:units[/tex]
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[tex]\large\sf\underline{Solution:}[/tex]
Determine the length from point P to point Q using the given formula.
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\bold{formula : } \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \\ \boxed{\rm D= \sqrt{(x_2 - x_1 {)}^{2} + (y_2 - y_1 {)}^{2} } }\end{gathered} \end{gathered}\end{gathered} \end{gathered} [/tex]
- [tex]\tt{(x_1, y_1) = (3,5) }[/tex]
- [tex]\tt{(x_2, y_2) = (3,-2) }[/tex]
Substitute in the two values of x and y coordinates.
- [tex]\rm PQ = \sqrt{(3 \:- \:3{)}^{2} + (-2\:-\:5{)}^{2} }[/tex]
- [tex]\rm PQ = \sqrt{(0 {)}^{2} + (-7{)}^{2} }[/tex]
- [tex]\rm PQ = \sqrt{(0) + (49)}[/tex]
- [tex]\rm PQ = \sqrt{49}[/tex]
Therefore, the distance between point P to point Q is 7 units
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