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Find the distance between the points (4,6)(4,6) and (8,3)(8,3).\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline__\_\_ units

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Full solution

Q. Find the distance between the points (4,6)(4,6) and (8,3)(8,3).\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline__\_\_ units
  1. Initialize Points: To find the distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), we use the distance formula: (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}. For the points (4,6)(4,6) and (8,3)(8,3), we have (x1,y1)=(4,6)(x_1, y_1) = (4, 6) and (x2,y2)=(8,3)(x_2, y_2) = (8, 3).
  2. Calculate x-coordinate difference: First, calculate the difference in the x-coordinates: (x2−x1)=(8−4)=4(x_2 - x_1) = (8 - 4) = 4.
  3. Calculate y-coordinate difference: Next, calculate the difference in the y-coordinates: (y2−y1)=(3−6)=−3(y_2 - y_1) = (3 - 6) = -3. Since we are going to square this value, the negative sign will not affect the result.
  4. Square the differences: Now, square the differences: (x2−x1)2=42=16(x_2 - x_1)^2 = 4^2 = 16 and (y2−y1)2=(−3)2=9(y_2 - y_1)^2 = (-3)^2 = 9.
  5. Add squared differences: Add the squared differences: 16+9=2516 + 9 = 25.
  6. Find the distance: Finally, take the square root of the sum to find the distance: 25=5\sqrt{25} = 5 units.

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