6 7 Midpoint of a Line Segment OBJECTIVE

6 -7: Midpoint of a Line Segment OBJECTIVE: You will find the coordinates of the midpoint of a line segment in the coordinate plane. • line segment - a piece of a line defined by two end-points • midpoint of a line segment - the point half way between the two end points To find the midpoint, you go half the distance in the x-direction and half the distance in the y-direction. To find the midpoint is a simple process: (1) Find the average of the x-coordinates, (2) Find the average of the y-coordinates, (3) The midpoint is then (x-average, y-average). © William James Calhoun, 2001

6 -7: Midpoint of a Line Segment 6. 7. 1 MIDPOINT OF A LINE SEGMENT ON A COORDINATE PLANE The coordinates of the midpoint of a line segment whose endpoints are at (x 1, y 1) and (x 2, y 2) are given by B (2, 5) M (-1, 2) To get from point A to point B, you would go: 6 units right, then 6 units up. Going half-way would be: 3 units right, then 3 units up. A (-4, -1) So the midpoint would be the blue dot at (-1, 2). Notice: (-4 + 2)/2 = -1, and (-1 + 5)/2 = 2. © William James Calhoun, 2001

6 -7: Midpoint of a Line Segment EXAMPLE 1: Find the coordinates of the midpoint of a segment with the endpoints (3, -8) and (-4, 2). Use the formula: midpoint = That is it. © William James Calhoun, 2001

6 -7: Midpoint of a Line Segment EXAMPLE 2: Find the coordinates of the other endpoint of a segment if one endpoint is (2, 6) and the midpoint is (-4, 2). The problem gives the x 1, y 1, and the average of the x’s and y’s. From the formula: and Solve for x 2. -2 -2 Solve for y 2. -6 -6 Take these values and write them as an ordered pair. Answer: (-10, -2). © William James Calhoun, 2001

6 -7: Midpoint of a Line Segment EXAMPLE 2: Find the coordinates of the other endpoint of a segment if one endpoint is (2, 6) and the midpoint is (-4, 2). Yes, it is the same example. Here is the CPM of finding the other endpoint. Endpoint #1 (2, 6) -6 -4 Midpoint (-4, 2) -6 -4 Endpoint #2 ( -10, -2 ) Look at the x-values. To get to -4 from 2, what must you add or subtract? subtract 6 Do it again. Look at the y-values. To get to 2 from 6, what must you add or subtract? subtract 4 Do it again. There is your answer. © William James Calhoun, 2001