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Find the distance between the points (3,1)(3,1) and (9,9)(9,9).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\newline__\_\_ units

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Q. Find the distance between the points (3,1)(3,1) and (9,9)(9,9).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\newline__\_\_ units
  1. Identify Coordinates: Identify the coordinates of the two points.\newlineWe have Point A (3,1)(3, 1) and Point B (9,9)(9, 9). From these points, we can determine the values of x1x_1, y1y_1, x2x_2, and y2y_2.\newlinex1=3x_1 = 3, y1=1y_1 = 1, x2=9x_2 = 9, y2=9y_2 = 9.
  2. Apply Distance Formula: Apply the distance formula.\newlineThe distance formula is d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. We will substitute the values of x1x_1, y1y_1, x2x_2, and y2y_2 into this formula.\newlined=(9−3)2+(9−1)2d = \sqrt{(9 - 3)^2 + (9 - 1)^2}.
  3. Calculate Differences: Calculate the differences and square them.\newlineCalculate (9−3)2(9 - 3)^2 and (9−1)2(9 - 1)^2.\newline(9−3)2=62=36(9 - 3)^2 = 6^2 = 36,\newline(9−1)2=82=64(9 - 1)^2 = 8^2 = 64.
  4. Add Squares: Add the squares together.\newlineAdd 3636 and 6464 to get the sum under the square root.\newline36+64=10036 + 64 = 100.
  5. Take Square Root: Take the square root of the sum to find the distance.\newlined=100d = \sqrt{100}.\newlineSince the square root of 100100 is 1010, the distance dd is 1010.\newlined=10d = 10 units.

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