Question - Calculating Distance Between Two Points in a Coordinate Plane
Solution:
To find the distance between two points, we can use the formula for the distance $$ d $$ between two points $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$ in the coordinate plane:\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]The points given are $$ (-3, -4) $$ and $$ (-10, -9) $$. Let's plug these coordinates into the formula:\[ d = \sqrt{(-10 - (-3))^2 + (-9 - (-4))^2} \]\[ d = \sqrt{(-10 + 3)^2 + (-9 + 4)^2} \]\[ d = \sqrt{(-7)^2 + (-5)^2} \]\[ d = \sqrt{49 + 25} \]\[ d = \sqrt{74} \]Now, let's find the square root of 74.\[ d \approx 8.602 \]Rounded to the nearest tenth, the distance is approximately 8.6 units.
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