Question

show what you know
if the points are (1, 2) and (4, 6), what is the distance between them?
5 units
4 units
7 units
6 units

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(1,2)\) and \((x_2,y_2)=(4,6)\)

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute the values: \(d=\sqrt{(4 - 1)^2+(6 - 2)^2}\)

Step3: Calculate the differences

\(x_2 - x_1=4 - 1 = 3\), \(y_2 - y_1=6 - 2 = 4\)

Step4: Square the differences

\((x_2 - x_1)^2=3^2 = 9\), \((y_2 - y_1)^2=4^2 = 16\)

Step5: Sum the squares

\((x_2 - x_1)^2+(y_2 - y_1)^2=9 + 16=25\)

Step6: Take the square root

\(d=\sqrt{25}=5\)

Answer:

5 units