Question

question 9 of 10 what is the approximate distance between the points (-5, 1) and (-2, 3) on a coordinate grid? a. 3.61 units b. 3.32 units c. 7.81 units d. 2.23 units

Explanation:

Step1: Recall the distance formula

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Identify the coordinates

Here, \(x_1=-5\), \(y_1 = 1\), \(x_2=-2\), \(y_2=3\).

Step3: Substitute into the formula

First, calculate \(x_2 - x_1=-2-(-5)=-2 + 5 = 3\) and \(y_2 - y_1=3 - 1=2\).
Then, \(d=\sqrt{(3)^2+(2)^2}=\sqrt{9 + 4}=\sqrt{13}\).

Step4: Approximate \(\sqrt{13}\)

We know that \(3^2 = 9\) and \(4^2=16\), so \(\sqrt{13}\) is between 3 and 4. Calculating \(\sqrt{13}\approx3.61\).

Answer:

A. 3.61 units