alleryThe distance between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ in the coordinate plane is
A$(x_2-x_1)+(y_2-y_1)$
B$\sqrt{(x_2-x_1)^2-(y_2-y_1)^2}$
C$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
D$(x_2-x_1)^2+(y_2-y_1)^2$
Answer & Solution
Correct answer: C. $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
The horizontal and vertical changes between the points are $x_2-x_1$ and $y_2-y_1$.
Applying the Pythagoras theorem gives $PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
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