Distance Distance – The length of a segment, found by using the coordinates of the endpoints. If the segment is part of a number line (either horizontal or vertical), simply subtract the coordinates – in any order – and take the absolute value of your answer. d= |a – b| or |b – a|

Distance If the segment is on a coordinate plane, then subtract the x-coordinates to find horizontal distance and the y-coordinates to find vertical distance. Use those two distances in conjunction with the Pythagorean Theorem to find the distance. The distance formula summarizes this process:

Midpoint Midpoint – The point halfway between the endpoints of the segment. If X is the midpoint of segment AB, then AX = XB. When finding the midpoint for a segment that is part of a number line, simply average the coordinates of the endpoints.

Midpoint When finding the midpoint of a segment on a coordinate plane, find the coordinates of the midpoint by averaging the x-coordinates of the endpoints and the y-coordinates of the endpoint independently.

Use the number line to find AX. Answer: 8 Example 3-1b

Find the distance between A(–3, 4) and M(1, 2). Answer: Example 3-2d

b. Find the coordinates of the midpoint of for X(–2, 3) and Y(–8, –9). a. The coordinates on a number line of Y and O are 7 and –15, respectively. Find the coordinate of the midpoint of . b. Find the coordinates of the midpoint of for X(–2, 3) and Y(–8, –9). Answer: –4 Answer: (–5, –3) Example 3-3c

Find the coordinates of R if N(8, –3) is the midpoint of Find the coordinates of R if N(8, –3) is the midpoint of and S has coordinates (–1, 5). Answer: (17, –11) Example 3-4c

Multiple-Choice Test Item What is the measure of Multiple-Choice Test Item What is the measure of if B is the midpoint of ? A 1 B 3 C 5 D 10 Answer: B Example 3-5e