Question

when graphed on a coordinate plane beths house is located at (4, 3) and the coffee shop is located at the point (-2, -1). what is the distance from beths house to the coffee shop? each grid line on the coordinate plane represents 1 mile. 52 miles √52 miles √8 miles 10 miles

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(4,3)\) and \((x_2,y_2)=(-2,-1)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(-2 - 4)^2+(-1 - 3)^2}\)

Step3: Simplify the expression

First, calculate \((-2 - 4)=-6\) and \((-1 - 3)=-4\)
Then \((-6)^2 = 36\) and \((-4)^2=16\)
\(d=\sqrt{36 + 16}=\sqrt{52}\)

Answer:

\(\sqrt{52}\text{ miles}\)