Question

which field frequently uses the distance formula for design and layout? a. literature b. history c. urban planning d. music for points (2, 3) and (6, 7), what is the calculated distance? a. $sqrt{20}$ b. $sqrt{32}$ c. 6 d. 5

Explanation:

Step1: Recall the distance - formula applications

The distance formula is used for measuring distances between points. Urban planning involves designing and laying out cities, which requires measuring distances between different locations. Literature, history, and music do not frequently use the distance formula for design and layout.

Step2: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Given \((x_1,y_1)=(2,3)\) and \((x_2,y_2)=(6,7)\), we substitute the values: \(d=\sqrt{(6 - 2)^2+(7 - 3)^2}=\sqrt{4^2+4^2}=\sqrt{16 + 16}=\sqrt{32}\).

Answer:

1. c. Urban planning
2. b. \(\sqrt{32}\)