Question

calculate the distance between the points c=(2, -7) and e=(5, -3) in the coordinate plane.give an exact answer (not a decimal approximation).

Explanation:

Step1: Identify the coordinates

Given \( C=(2,-7) \) and \( E=(5,-3) \). Let \( (x_1,y_1)=(2,-7) \) and \( (x_2,y_2)=(5,-3) \).

Step2: Use the distance formula

The distance formula is \( d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
Substitute the values: \( x_2 - x_1=5 - 2 = 3 \), \( y_2 - y_1=-3-(-7)=-3 + 7 = 4 \).
Then \( d=\sqrt{(3)^2+(4)^2}=\sqrt{9 + 16}=\sqrt{25}=5 \).

Answer:

\( 5 \)