To correct the grammar and remove unnecessary words: Part B: If M is the midpoint of line segment CD and the coordinates of M are (2,7), what are the coordinates of point D?

Mathematics · High School · Thu Feb 04 2021

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The corrected and more concise version of the sentence would be: "If M is the midpoint of line segment CD and M's coordinates are (2, 7), what are the coordinates of point D?"

Extra: In geometry, the midpoint of a line segment is the point that is exactly halfway between the endpoints of the segment. If you know the coordinates of the midpoint M, and the coordinates of one of the endpoints (either C or D), you can find the coordinates of the other endpoint using the midpoint formula:

(Midpoint x-coordinate) = (x-coordinate of C + x-coordinate of D) / 2 (Midpoint y-coordinate) = (y-coordinate of C + y-coordinate of D) / 2

To find the coordinates of D if M is the midpoint, you rearrange the formulas:

x-coordinate of D = 2 * (Midpoint x-coordinate) - x-coordinate of C y-coordinate of D = 2 * (Midpoint y-coordinate) - y-coordinate of C

In a classroom setting, this concept is typically taught in a unit on coordinate geometry, which is a part of the algebra or geometry curriculum. Students learn how to apply the midpoint formula and may practice by solving problems that give them the midpoint and one endpoint and ask them to find the other endpoint.