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Wo nown 'shau your work\newlineFind the distance between the points \newline(−5,−10)(-5,-10) and \newline(−2,−6)(-2,-6).\newlineWhec your answer as a whole number or a filly simplified radical expression. Do not round. units\text{units}\newlineSubmit

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Q. Wo nown 'shau your work\newlineFind the distance between the points \newline(−5,−10)(-5,-10) and \newline(−2,−6)(-2,-6).\newlineWhec your answer as a whole number or a filly simplified radical expression. Do not round. units\text{units}\newlineSubmit
  1. Identify Coordinates and Formula: Identify the coordinates of the two points and the distance formula.\newlineThe coordinates are given as (−5,−10)(-5,-10) for the first point and (−2,−6)(-2,-6) for the second point. The distance formula is (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}.
  2. Substitute into Formula: Substitute the coordinates into the distance formula.\newlineUsing the points (−5,−10)(-5,-10) and (−2,−6)(-2,-6), we get:\newlineDistance = (−2−(−5))2+(−6−(−10))2\sqrt{(-2 - (-5))^2 + (-6 - (-10))^2}.
  3. Simplify Expression: Simplify the expression inside the square root.\newlineCalculate (−2−(−5))2(-2 - (-5))^2 which simplifies to (3)2(3)^2 and (−6−(−10))2(-6 - (-10))^2 which simplifies to (4)2(4)^2.\newlineDistance = (3)2+(4)2\sqrt{(3)^2 + (4)^2}.
  4. Calculate Squares: Calculate the squares of the numbers.\newline(3)2(3)^2 equals 99 and (4)2(4)^2 equals 1616.\newlineDistance = 9+16\sqrt{9 + 16}.
  5. Add and Simplify: Add the results inside the square root and simplify. 9+16\sqrt{9 + 16} simplifies to 25\sqrt{25}.
  6. Calculate Square Root: Calculate the square root of 2525.25\sqrt{25} equals 55.

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