geometry-endpoints

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Directions in my book say, "find the coordinates of the other ENDPOINT of a segment with the given endpoint and midpoint M."

example: R(2,6)
M(-1,1)


I really need help.

  • geometry-endpoints -

    I am assuming that (2,6) are the x and y coordinates of point R.

    If the coordinates of the midpoint are (-1,1), the other endpoint has a decrease in x of -3, and a decrease of y by 5. (The same as from R to M)

    That makes the coordinates of the other endpoint (-4, -4)

  • geometry-endpoints -

    One way it to subtract the x values 2-(-1) = 3. Since that is 1/2 the line segment, then -1 -3 = -4 for the x value of the end of the other segment. The value of the y segment is done similarly (6-1 = 5 and 1-5 = -4 so the coordinates of the other end point is (-4,-4). You can check these values by plugging the values into y = mx + b to see if all satisfy the equation.

  • geometry-endpoints -

    Oh. But I don't quite understand the process.

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