Question

find the distance between the two points rounding to the nearest tenth (if necessary). (0, 0) and (6, 8)

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step2: Identify coordinates

Here, \( x_1 = 0 \), \( y_1 = 0 \), \( x_2 = 6 \), \( y_2 = 8 \).

Step3: Substitute into formula

\( d = \sqrt{(6 - 0)^2 + (8 - 0)^2} = \sqrt{6^2 + 8^2} \)

Step4: Calculate squares

\( 6^2 = 36 \), \( 8^2 = 64 \), so \( d = \sqrt{36 + 64} \)

Step5: Sum inside square root

\( 36 + 64 = 100 \), so \( d = \sqrt{100} \)

Step6: Simplify square root

\( \sqrt{100} = 10 \)

Answer:

10