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Section 1.3: Using Midpoint and Distance Formulas
Warm-Up:
Average the following sets of numbers:
1. 4 and 12
2. -5, 10
3. List all perfect squares less than 100.
Rationalize the following radical expressions:
4.
27
5.
40
Questions from HW 1.2?!?!
Lesson Objectives
At the end of today’s lesson, you will be able to:
1) describe what it means for something to be a segment bisector.
2) combine the ideas of segment bisector and segment addition to solve various problems.
3) use the midpoint formula to find a missing coordinate.
4) find the distance between two given points on the coordinate plane.
Objective #1
Think about the word bicycle. What does it mean?
Using the same logic, what do you think it means to bisect a segment?
Very simply, a segment bisector is a point, line, ray, segment, or plane that cuts a segment in half.
Now, if a segment is cut in half, that means the bisector passes through what?
Ex.
Suppose ray CD bisects segment AB at point C. Furthermore, suppose the
the length of AB.
Ex.
Let M be the bisector of LN. Find LN.
Ex.
Line WX bisects
YZ
at point W. Find YZ if WZ =
inches.
14
AC = 3 cm. Find
Objective #3
Ex.
Find the midpoint of 2 and 10 on the number line.
Ex.
Find the midpoint of -11 and 9 on the number line.
Now that we’ve established how to find the midpoint on the number line, let’s take a look at how to
find the midpoint of two coordinates on the x-y plane.
Ex.
Find the midpoint of (0, 0) and (10, 8).
Rather than memorizing some formula, just know to find the midpoint of two coordinates,
AVERAGE THE X’S and AVERAGE THE Y’S!!!
Ex.
Find the midpoint of (-2, 4) and (14, -2).
Ex.
Suppose the midpoint of segment VW is M(-1, -2). Let W(4, 4)…find the coordinates of endpoint
V.
Objective #4
Discuss with your partner how to find the distance between two points on the number line.
So again, we know how to find the distance between two numbers on the number line, now we will
take a look at how to find the distance between two coordinates on the x-y plane.
Ex.
Find the distance between (0, 0) and (7, 8).
The distance formula is given by
y1) and (x2, y2).
x2  x1 2   y2  y1 2
, where your coordinates are (x1,
Ex.
What is the length of segment AB, where A(-3, 2) and B(1, -4)?
Additional examples?! Questions?! Comments?! Concerned?!
HW: Pg. 19 #4-20 (even), 25-27, 32-40(even), 43, 44 (Due Tuesday)