Question - Finding the Distance between Two Points
Solution:
To find the distance between the two points (9, 1) and (3, 10), you can use the distance formula, which is derived from the Pythagorean theorem:\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]Here, $$ (x_1, y_1) = (9, 1) $$ and $$ (x_2, y_2) = (3, 10) $$.Plugging in the values:\[ \text{Distance} = \sqrt{(3 - 9)^2 + (10 - 1)^2} \]\[ \text{Distance} = \sqrt{(-6)^2 + (9)^2} \]\[ \text{Distance} = \sqrt{36 + 81} \]\[ \text{Distance} = \sqrt{117} \]Now, simplify this to get the final answer:\[ \text{Distance} = \sqrt{117} \approx 10.82 \]The question asks to round decimals to the nearest tenth:\[ \text{Distance} \approx 10.8 \text{ units} \]
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