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K(5,3)K(5,3) and L(3,9)L(3,9) are the endpoints of a line segment. What is the midpoint MM of that line segment?\newlineWrite the coordinates as decimals or integers.\newlineM=(_,_)M = (\_,\_)

Full solution

Q. K(5,3)K(5,3) and L(3,9)L(3,9) are the endpoints of a line segment. What is the midpoint MM of that line segment?\newlineWrite the coordinates as decimals or integers.\newlineM=(_,_)M = (\_,\_)
  1. Identify midpoint formula: Identify the midpoint formula for a line segment.\newlineThe midpoint of a line segment with endpoints (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the formula:\newlineMidpoint M=(x1+x22,y1+y22)M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right).
  2. Apply formula to endpoints: Apply the midpoint formula to the given endpoints K(5,3)K(5,3) and L(3,9)L(3,9). Substitute the given coordinates into the midpoint formula: M=(5+32,3+92)M = \left(\frac{5 + 3}{2}, \frac{3 + 9}{2}\right).
  3. Calculate midpoint coordinates: Calculate the coordinates of the midpoint MM.M=(5+32,3+92)=(82,122)=(4,6)M = \left(\frac{5 + 3}{2}, \frac{3 + 9}{2}\right) = \left(\frac{8}{2}, \frac{12}{2}\right) = (4, 6).

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