Pre-Algebra Chapter 9
Pre-Algebra Chapter 9
Pre-Algebra Chapter 9
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The Distance and<br />
Midpoint Formulas<br />
Vocabulary<br />
• Distance Formula<br />
• midpoint<br />
• Midpoint Formula<br />
• Use the Distance Formula to determine lengths on a coordinate plane.<br />
• Use the Midpoint Formula to find the midpoint of a line segment on the<br />
coordinate plane.<br />
is the Distance Formula related<br />
to the Pythagorean Theorem?<br />
The graph of points N(3, 0) and M(4, 3) is<br />
y<br />
M(4, 3)<br />
shown. A horizontal segment is drawn<br />
from M, and a vertical segment is drawn<br />
from N. The intersection is labeled P.<br />
O<br />
a. Name the coordinates of P.<br />
b. Find the distance between M and P.<br />
c. Find the distance between N and P.<br />
d. Classify MNP.<br />
e. What theorem can be used to find the distance between M and N?<br />
f. Find the distance between M and N.<br />
P<br />
N(3, 0) x<br />
THE DISTANCE FORMULA Recall that a line segment is a part of a line.<br />
It contains two endpoints and all of the points between the endpoints.<br />
M<br />
y<br />
A line segment is named<br />
by its endpoints.<br />
O<br />
N<br />
x<br />
The segment can be<br />
written as MN or NM.<br />
To find the length of a segment on a coordinate plane, you can use the<br />
Distance Formula, which is based on the Pythagorean Theorem.<br />
Study Tip<br />
Look Back<br />
To review the notation<br />
(x 1<br />
, y 1<br />
) and (x 2<br />
, y 2<br />
), see<br />
Lesson 8-4.<br />
• Words<br />
• Model<br />
Distance Formula<br />
The distance d between two points with coordinates (x 1<br />
, y 1<br />
) and<br />
(x 2<br />
, y 2<br />
), is given by d (x x 2<br />
1<br />
) 2 (y 2<br />
.<br />
y 1<br />
) 2<br />
y (x 2 , y 2<br />
)<br />
(x 1 , y 1<br />
)<br />
d<br />
O x<br />
Concept Check<br />
How is a line segment named?<br />
466 <strong>Chapter</strong> 9 Real Numbers and Right Triangles
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