Question

What is the approximate distance between points A and B? A coordinate grid is shown from negative 5 to 0 to 5 on both axes at increments of 1. The ordered pair 4, 3 is labeled as A, and the ordered pair negative 2, negative 4 is labeled as B 3.61 9.22 10.35 12.62

Answer 1

Answer:

$\large \boxed{9.22}$

Step-by-step explanation:

The formula for the distance between two points is

$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$

x₂ - x₁ = 4 - (-2) = 9

y₂ - y₁ = 3 - (-4) = 7

The formula, in effect, creates a right triangle, so we can use the Pythagorean theorem to calculate the distance.

$\begin{array}{rcl}AB & = & \sqrt{6^{2} + 7^{2}}\\& = & \sqrt{36 + 49}\\& = & \sqrt{85}\\& \approx & \mathbf{9.220} \end{array}\\\text{The approximate distance between the points is \large \boxed{\mathbf{9.220}} }$