Question

find the distance between the points g(-5, 4) and h(2, 6). 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: \( d=\sqrt{(7)^2+(2)^2}=\sqrt{49 + 4}=\sqrt{53} \).

Answer:

\(\sqrt{53}\)