The distance between points P(1, 2) and Q(-3, 6) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4\(\sqrt{2}\)
The distance formula \(PQ=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}\) is Pythagoras’ theorem: the differences in \(x\) and in \(y\) are the two shorter sides of a right triangle with PQ as its hypotenuse, as the figure below shows.
Difference in \(x\): \(-3-1=-4\), a horizontal side of 4 units
Difference in \(y\): \(6-2=4\), a vertical side of 4 units
Hypotenuse: \(PQ=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}\)
