Question

Find the distance between the points (0,−4) and (−3,3) .Give an exact answer (no decimals).

Answer 1

As you can see above the distance between two points (green) is the hypotenuse of a right triangle where the x-distance between the points is a Leg (blue) and the y-distance between the points is the other leg (red); using the pythagorean theorem you can find the distance between the points (find the hypotenuse of the right triangle formed)

Use the next formula to find the distance between two points:

`d=√(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

For the given points: (0,−4) and (−3,3)

`\begin{gathered} d=√(\left(-3-0\right)^2+\left(3-\left(-4\right)\right)^2) \\ d=√(\left(-3\right)^2+\left(7\right)^2) \\ d=√(9+49) \\ d=√(58) \end{gathered}`Then, the distance between (0,−4) and (−3,3) is √58