Question

Use the pythagorean theorem to find the distance between (2,8) and (-8,2) A. 16.0 B. 4.0 C. 12.3 D. 11.7

Answer 1

Using the Pythagorean theorem, the distance between two points (x1, y1) and (x2, y2) is gotten as follows:

`\begin{gathered} d^2=(x_2-x_1)^2+(y_2-y_1)^2 \\ \text{Thus:} \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}`

Since we have the two coordinates: (2, 8) and (-8, 2)

where:

(x1, y1)= (2, 8)

(x2, y2) = (-8, 2)

Therefore, the distance between them is:

`\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{((-8)_{}-2_{})^2+(2-8)^2} \\ d=\sqrt[]{((-10_{})^2+(-6)^2} \\ d=\sqrt[]{100+36} \\ d=\sqrt[]{136} \\ d=11.66 \\ d=11.7\text{ (to one decimal place)} \end{gathered}`

Therefore, the distance between the two p is: 11.7

Correct option is: Option D