Midpoint and Distance Formulas

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Presentation transcript:

Midpoint and Distance Formulas

Definition The midpoint of a segment is the point that divides the segment into two congruent segments.

Midpoint Formula The coordinates of the midpoint of a segment are the averages of the x-coordinates and of the y-coordinates of the endpoints.

Finding a Midpoint Find the midpoint between the endpoints (1, 7) & (3, -4). Find the midpoint between the endpoints (2, 5) & (-3, 9)

Finding an Endpoint If the midpoint of segment AB is (2, 3) and A is at (-1, 5), where is B located? If the midpoint of segment CD is (0, -2) and D is at (3, 4), where is C located?

Distance Formula The distance formula is used to compute the distance between two points in a coordinate plane. It is given by:

Finding the Distance Find the distance between the points (1, 4) and (-2, 8).

Partitioning a line segment in 1-dimension A ratio of a:b means we are partitioning the segment into “a+b” parts 1) find the length of the segment 2) Multiply by the scaler “a/(a+b)” 3) Add your answer to the first endpoint to determine the coordinate of the partition

Example: The endpoints of segment PQ are -3 and 7. Find the coordinates of the point P that partitions the segment in the ratio 3:5

“Taxicab” Distance Formula Find the taxicab distance between (-2, 8) & (1,4) by graphing.

Practice A2 P.19 #3-22