Determine the distance from point A(4, -3) B(6, -2)

Answer 1

Carlos,

The key to answering this question is to realize that the Pythagorean Theorem can help you. These two points can be considered to form the vertices of a hypotenuse of a right triangle, something like the one shown below (Wyzant made me delete the triangle.)

A(4, -3) B(6, -2)

The distance between these two given points is the hypotenuse of the triangle, h. The Pythagorean Theorem says that: h² = a² + b²

^{So, we need a and b so that we can calculate h.}

^{To determine a, we subtract the two y-coordinates.}

^{–2 – (–3) = –2 + 3 = 1 = a}

^{To determine b, we subtract the two x-coordinates.}

^{6 – 4 = 2 = b}

^{Now, we fill in the values of a and b that we have calculated in the Pythagorean Theorem equation.}

h² = a² + b²

h² = 1² + 2²

h² = 1 + 4

h² = 5

h = √5

√5 is the distance between the two points, A and B.