Geo 13.notebook August 24, 2012 1-3, Distance and Midpoints Today you will... - Find the distance between two points. - Find the midpoint of a segment. Distance Between Two Points The distance between two points is the length of the segment with those points as its endpoints. The order in which you name the endpoints is not important when calculating distance. To find the distance between two points in the coordinate plane, you can form a right triangle. Recall that the Pythagorean Theorem is often expressed as a 2 + b2 = c2 where a and b are the measures of the shorter sides (legs) and c is the measure of the longest side (hypotenuse). Geo 13.notebook August 24, 2012 Distance Formula (in Coordinate Plane) Find the distance between each pair of points. E (-5, 6) and F (8, -4) J(4, 3) and K(-3, -7) Midpoint of a Segment Midpoint Formula (in a Coordinate Plane) The midpoint of a segment is the point halfway between the endpoints of the segment. You can find the midpoint of a segment on a number line by finding the mean, or the average, of the coordinates of its endpoints. You can find the midpoint of a segment on the coordinate plane by finding the average of the x-coordinates and of the y-coordinates of the endpoints. Find the coordinates of the midpoint of a segment with the given coordinates. You can also find the coordinates of the endpoint of a segment if you know the coordinates of its other endpoint and its midpoint. A(5, 12) and B(-4, 8) C(-8, -2) and D (5, 1) To do this, we use the midpoint formula and work backward! Geo 13.notebook August 24, 2012 Find the coordinates of the missing endpoint if P is the midpoint of EG. E(-8, 6) and P(-5, 10) P(-1, 3) and G(5, 6) You can use algebra to find a missing measure or value in a figure that involves the midpoint of a segment.
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