Question

question 10.
what is the approximate distance between the points (6, 3) and (4, 8)?
a. 1.1 units
b. 7 units
c. 2.5 units
d. 5.4 units

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(6,3)\) and \((x_2,y_2)=(4,8)\)

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

Substitute the values: \(d=\sqrt{(4 - 6)^2+(8 - 3)^2}=\sqrt{(-2)^2+5^2}=\sqrt{4 + 25}=\sqrt{29}\)

Step3: Calculate the approximate value

\(\sqrt{29}\approx5.4\) (since \(5^2 = 25\) and \(6^2=36\), and \(29\) is closer to \(25\) than \(36\), and using a calculator \(\sqrt{29}\approx5.385\approx5.4\))

Answer:

D. \(5.4\) units