What is the distance between the points \(A(1,\,-4)\) and \(B(-4,\,8)\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 13 units
The distance between \((x_1,\,y_1)\) and \((x_2,\,y_2)\) is \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\): Pythagoras’ theorem on the horizontal and vertical gaps between the points.
Horizontal gap: \(-4-1=-5\), and \((-5)^2=25\)
Vertical gap: \(8-(-4)=12\), and \(12^2=144\)
\(AB^2=25+144=169\)
\(AB=\sqrt{169}=13\) units
