Question

calculate the distance between the points ( k = (-4, 6) ) and ( n = (-1, 3) ) in the coordinate plane. round your answer to the nearest hundredth.

Explanation:

Step1: Identify the coordinates

Let \( (x_1,y_1)=(-4,6) \) and \( (x_2,y_2)=(-1,3) \).

Step2: Use the distance formula

The distance formula is \( d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
Substitute the values: \( x_2 - x_1=-1-(-4)=3 \), \( y_2 - y_1=3 - 6=-3 \).
Then \( d=\sqrt{(3)^2+(-3)^2}=\sqrt{9 + 9}=\sqrt{18} \).

Step3: Simplify and round

\( \sqrt{18}\approx4.24 \) (rounded to the nearest hundredth).

Answer:

\(4.24\)