Question

find the distance between the points g(-5, 4) and h(2, 6). answer in simplest exact form. the exact distance between the two points is \boxed{}.

Explanation:

Step1: Recall the distance formula

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1=-5,y_1 = 4,x_2=2,y_2=6\).

Step2: Substitute the values into the formula

First, calculate \(x_2 - x_1=2-(-5)=2 + 5=7\) and \(y_2 - y_1=6 - 4 = 2\). Then, substitute these into the formula: \(d=\sqrt{(7)^2+(2)^2}\).

Step3: Simplify the expression

Calculate \((7)^2 = 49\) and \((2)^2=4\). Then, \(d=\sqrt{49 + 4}=\sqrt{53}\).

Answer:

\(\sqrt{53}\)