Question

i will use the distance formula to find the perimeter & area of coordinate polygons engage 1. which is the closest to the distance between the points (1, 3) and (5, 7)? a. 7.8 units b. 5.7 units c. 2.1 units d. 4.8 units

Explanation:

Step1: Recall distance formula

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

Step2: Identify coordinates

Here, \(x_1 = 1\), \(y_1 = 3\), \(x_2 = 5\), \(y_2 = 7\).

Step3: Substitute into formula

Substitute the values into the formula: \(d=\sqrt{(5 - 1)^2+(7 - 3)^2}=\sqrt{4^2 + 4^2}=\sqrt{16 + 16}=\sqrt{32}\).

Step4: Simplify \(\sqrt{32}\)

\(\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}\approx4\times1.414 = 5.656\approx5.7\) units.

Answer:

B. 5.7 units