Question

1. on a maps coordinate grid, panthersville is located at (- 3, 2) and heel city is located at (4, 8). falcanton is the midpoint between panthersville and heel city. what is the distance from panthersville to falcanton? (one map unit equals one mile.

Explanation:

Step1: Calculate the distance between Panthersville and Heel City

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \((x_1,y_1)=(-3,2)\) and \((x_2,y_2)=(4,8)\).

$$
LATEXBLOCK0
$$

Step2: Find the distance from Panthersville to Falcanton

Since Falcanton is the mid - point, the distance from Panthersville to Falcanton is half of the distance from Panthersville to Heel City. So, \(d_{PF}=\frac{\sqrt{85}}{2}\approx\frac{9.22}{2}=4.61\) miles.

Answer:

The distance from Panthersville to Falcanton is \(\frac{\sqrt{85}}{2}\approx4.61\) miles.