Transcript Example 3-1b

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:
d  ( x1  x2 )2  ( y1  y2 ) 2
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.
ab
M(
)
2
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.
x1  x2 y1  y2
M(
,
)
2
2
Use the number line to find AX.
Answer: 8
Find the distance between A(–3, 4) and M(1, 2).
Answer:
a. The coordinates on a number line of Y and O are
7 and –15, respectively. Find the coordinate of the
midpoint of
.
Answer: –4
b. Find the coordinates of the midpoint of
for X(–2, 3) and Y(–8, –9).
Answer: (–5, –3)
Find the coordinates of R if N(8, –3) is the midpoint
of
and S has coordinates (–1, 5).
Answer: (17, –11)
Multiple-Choice Test Item
What is the measure of
if B is the midpoint of
A1
Answer: B
B3
C5
D 10
?