Question - Calculating Distance Between Two Points in a Plane
Solution:
To find the distance between two points in a plane, you can use the distance formula, which is derived from the Pythagorean theorem. The distance $$ d $$ between two points $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$ is given by:\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]For the points $$ (1, -7) $$ and $$ (-6, 2) $$, we can calculate the distance as follows:Let $$ x_1 = 1 $$, $$ y_1 = -7 $$, $$ x_2 = -6 $$, and $$ y_2 = 2 $$.\[ d = \sqrt{(-6 - 1)^2 + (2 - (-7))^2} \]\[ d = \sqrt{(-7)^2 + (9)^2} \]\[ d = \sqrt{49 + 81} \]\[ d = \sqrt{130} \]\[ d \approx 11.4 \] (rounded to the nearest tenth)So the distance between the points $$ (1, -7) $$ and $$ (-6, 2) $$ is approximately 11.4 units.
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