### Lesson 1-3 Distance and Midpoint

```Content Standards
G.CO.1 Know precise definitions of angle, circle,
perpendicular line, parallel line, and line segment, based
on the undefined notions of point, line, distance along a
line, and distance around a circular arc.
G.CO.12 Make formal geometric constructions with a
variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic
geometric software, etc.).
Mathematical Practices
2 Reason abstractly and quantitatively.
7 Look for and make use of structure.
You graphed points on the coordinate plane.
• Find the distance between two points.
• Find the midpoint of a segment.
• distance
• irrational number
• midpoint
• segment bisector
Find Distance on a Number Line
Use the number line to find QR.
The coordinates of Q and R are –6 and –3.
QR = | –6 – (–3) |
= | –3 | or 3
Distance Formula
Simplify.
Use the number line to find AX.
Switching both coordinates in the formula will give the same
result for the distance. See below.
d 
( x1  x 2 )  ( y 1  y 2 )
2
2
Find Distance on a Coordinate Plane
Find the distance between E(–4, 1) and F(3, –1).
(x1, y1) = (–4, 1) and
(x2, y2) = (3, –1)
Find Distance on a Coordinate Plane
Check Graph the ordered pairs
and check by using the
Pythagorean Theorem.
Draw a sketch of this graph on your paper.
Find Distance on a Coordinate Plane
.
Find the distance between A(–3, 4) and M(1, 2) using
the distance formula.
Chapter 1 Overview Video
Distance and Midpoint Skills Packet
Do 7 and 8 (find the distance only)
Now let’s do the Reach test questions 1-3
Find Midpoint in Coordinate Plane
Class Assignment - 8 minutes
Distance and Midpoint Skills Packet
Do 4, 5 and 8 (Find the midpoint only)
Find the Coordinates of an Endpoint
Let D be (x1, y1) and F be (x2, y2) in the Midpoint
Formula.
(x2, y2) = (–5, –3)
Write two equations to find the coordinates of D.
Find the Coordinates of an Endpoint
Midpoint Formula
Midpoint Formula
Answer: The coordinates of D are (–7, 11).
5 minutes
Skills Packet
Do 9 and 10
Use Algebra to Find Measures
Understand
You know that Q is the midpoint of PR,
and the figure gives algebraic measures
for QR and PR. You are asked to find
the measure of PR.
Use Algebra to Find Measures
Plan
Because Q is the midpoint, you know
that
Use this equation and the algebraic measures to find a
value for x.
Solve
Subtract 1 from each side.
Use Algebra to Find Measures
Original measure
• Constructions p. 30 ‘Bisect a Segment
• HW Skills Packet 1-7, 12-16 all
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