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The midpoint M of KL has coordinates (6, 4). Point K has coordinates (5, 5). Find the coordinates of point L.

User Rupello
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Final answer:

The coordinates of point L, given the midpoint M is at (6, 4) and one endpoint K is at (5, 5), are found to be (7, 3) by solving two equations based on the definition of a midpoint.

Step-by-step explanation:

The question involves finding the coordinates of point L given that it is the other endpoint of a line segment with midpoint M at (6, 4), and one endpoint K at (5, 5). To find the coordinates of point L, we will use the concept of a midpoint, which is the average of the coordinates of two endpoints. Since M is the midpoint of KL, we can write two equations:

  • The midpoint's x-coordinate is the average of the x-coordinates of K and L: (5 + xL)/2 = 6.
  • The midpoint's y-coordinate is the average of the y-coordinates of K and L: (5 + yL)/2 = 4.

By solving these equations, we find xL and yL which are the x and y coordinates of point L, respectively.

Solving the first equation for xL:
(5 + xL)/2 = 6
5 + xL = 12
XL = 12 - 5
xL = 7

Solving the second equation for yL:
(5 + yL)/2 = 4
5 + yL = 8
yL = 8 - 5
yL = 3

Therefore, the coordinates of point L are (7, 3).

User John Plummer
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