The midpointM of KL has coordinates (7,4). Point L has coordinates (4,2). Find the coordinates of point K.Write the coordinates as decimals or integers.K=(_,_)
Q. The midpoint M of KL has coordinates (7,4). Point L has coordinates (4,2). Find the coordinates of point K.Write the coordinates as decimals or integers.K=(_,_)
Understand midpoint formula: Understand the midpoint formula and the given information.The midpoint formula for a line segment with endpoints (x1,y1) and (x2,y2) is given by:Midpoint = (2x1+x2,2y1+y2)Given: Midpoint M(7,4) and one endpoint L(4,2). We need to find the other endpoint K(x1,y1).
Set up equations: Set up the equations for the midpoint based on the given coordinates.We have the midpoint M(7,4) and one endpoint L(4,2). Let's denote the coordinates of point K as (x1,y1).Using the midpoint formula, we get two equations:7=2x1+44=2y1+2
Solve for x-coordinate: Solve for the x-coordinate of point K.From the first equation:7=2x1+4Multiply both sides by 2 to get rid of the fraction:14=x1+4Subtract 4 from both sides to solve for x1:14−4=x110=x1The x-coordinate of point K is 10.
Solve for y-coordinate: Solve for the y-coordinate of point K.From the second equation:4=2(y1+2)Multiply both sides by 2 to get rid of the fraction:8=y1+2Subtract 2 from both sides to solve for y1:8−2=y16=y1The y-coordinate of point K is 6.
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