Question

k = (-3, 4)
l = (5, 0)

Explanation:

Step1: Identify the problem type

This is a problem about finding the distance between two points \( K(-3, 4) \) and \( L(5, 0) \) in a coordinate plane, which falls under Geometry (a subfield of Mathematics). We use the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).

Step2: Assign coordinates

Let \( (x_1,y_1)=(-3,4) \) and \( (x_2,y_2)=(5,0) \).

Step3: Substitute into the distance formula

First, calculate \( x_2 - x_1 = 5-(-3)=5 + 3 = 8 \) and \( y_2 - y_1 = 0 - 4=-4 \).

Then, square these values: \( (x_2 - x_1)^2=8^2 = 64 \) and \( (y_2 - y_1)^2=(-4)^2 = 16 \).

Step4: Sum the squared values and take the square root

Sum: \( 64+16 = 80 \). Then, \( d=\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}\approx8.94 \) (if we want a decimal approximation).

Answer:

The distance between points \( K \) and \( L \) is \( 4\sqrt{5} \) (or approximately \( 8.94 \)).