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The midpoint MM of KL\overline{KL} has coordinates (7,4)(7,\,4). Point LL has coordinates (4,2)(4,\,2). Find the coordinates of point KK.\newlineWrite the coordinates as decimals or integers.\newlineK=(_,_)K = (\_,\,\_)

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Q. The midpoint MM of KL\overline{KL} has coordinates (7,4)(7,\,4). Point LL has coordinates (4,2)(4,\,2). Find the coordinates of point KK.\newlineWrite the coordinates as decimals or integers.\newlineK=(_,_)K = (\_,\,\_)
  1. Understand midpoint formula: Understand the midpoint formula and the given information.\newlineThe midpoint formula for a line segment with endpoints (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by:\newlineMidpoint = (x1+x22,y1+y22)\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)\newlineGiven: Midpoint M(7,4)M(7, 4) and one endpoint L(4,2)L(4, 2). We need to find the other endpoint K(x1,y1)K(x_1, y_1).
  2. Set up equations: Set up the equations for the midpoint based on the given coordinates.\newlineWe have the midpoint M(7,4)M(7, 4) and one endpoint L(4,2)L(4, 2). Let's denote the coordinates of point KK as (x1,y1)(x_1, y_1).\newlineUsing the midpoint formula, we get two equations:\newline7=x1+427 = \frac{x_1 + 4}{2}\newline4=y1+224 = \frac{y_1 + 2}{2}
  3. Solve for x-coordinate: Solve for the x-coordinate of point K.\newlineFrom the first equation:\newline7=x1+427 = \frac{x_1 + 4}{2}\newlineMultiply both sides by 22 to get rid of the fraction:\newline14=x1+414 = x_1 + 4\newlineSubtract 44 from both sides to solve for x1x_1:\newline144=x114 - 4 = x_1\newline10=x110 = x_1\newlineThe x-coordinate of point K is 1010.
  4. Solve for y-coordinate: Solve for the y-coordinate of point K.\newlineFrom the second equation:\newline4=(y1+2)24 = \frac{(y_1 + 2)}{2}\newlineMultiply both sides by 22 to get rid of the fraction:\newline8=y1+28 = y_1 + 2\newlineSubtract 22 from both sides to solve for y1y_1:\newline82=y18 - 2 = y_1\newline6=y16 = y_1\newlineThe y-coordinate of point K is 66.

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