Question

the points (-3, 7) and (5, 1) are plotted on a coordinate plane. what is the distance between the two points? enter the answer in the box.
box units

Explanation:

Step1: Recall 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 coordinates

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

Step3: Substitute into formula

First, calculate \(x_2 - x_1=5-(-3)=5 + 3=8\) and \(y_2 - y_1=1 - 7=-6\).
Then, \((x_2 - x_1)^2=8^2 = 64\) and \((y_2 - y_1)^2=(-6)^2=36\).
Sum these: \(64 + 36=100\).
Take the square root: \(d=\sqrt{100}=10\).

Answer:

10