to find distance on a number line, you can just count ... · to find distance on a number line, you...
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Section 1.3 Distance and Midpoints To find distance on a number line, you can just count the units between the two points.
TO FIND DISTANCE ON A NUMBER LINE
Ex 1 Use the number line to find each measure.
a. BD
b. AF
c. DG
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To find the distance between two points on a coordinate plane, you are going to use the distance formula.
DISTANCE FORMULA ON A COORDINATE PLANEThe distance d between points with coordinates and is given by
You can round your answers for the distance formula to the nearest tenth.
Ex 2 Use the distance formula to find the distance between R (5 , 1) and S ( 3, 3).
Ex 3 Find the distance between E(4 , 1) and F (3 , 1).
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Ex:
.
Ex 4 Use the Pythagorean Theorem to find the distance between each pair of points.
(HINT: When it says to use the Pythagorean Theorem, you can just use the distance formula and it is the same thing!)
The midpoint of a segment is the point halfway between the endpoints of the segment.
If B is the midpoint of AC, then AB = BC.
To find the midpoint of two points on a number line, just add the two numbers together and then divide by two.
TO FIND THE MIDPOINT ON A NUMBER LINEThe coordinates of the midpoint of a segment whose endpoints have coordinates a and b is
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Ex 5 Use the number line to find the coordinate of the midpoint of each segment.
a. DE
b. BC
c. AD
To find the coordinates of the midpoint between two points on the coordinate plane, you use the Midpoint Formula below:
MIDPOINT FORMULA ON A COORDINATE PLANEThe coordinates of the midpoint of a segment whose endpoints have coordinates and are
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Recall the formula from the previous page:
Ex 6 Find the coordinates of the midpoint of a segment having the given endpoints.
a. T (3 , 1) and U (5 , 3)
b. J (4, 2) and F (5, 2)
c. W (12, 7) and T(8,4)
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You can also find the coordinates of the endpoint of a segment if you know the coordinates of its other endpoint and its midpoint.
Ex 7 Find the coordinates of the missing endpoint given that E is the midpoint of DF.
a. F (5 , 8) and E (4 , 3)
b. F (2 , 9) and E (1 , 6)
c. D (3 , 8) and E (1 , 2)
Ex 8 What is the measure of PR if Q is the midpoint of PR?
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Assign Pgs. 25 27 # 2, 13 18, 23 45, 57, 59 62 Quiz on ______________
Any segment, line, or plane that intersects a segment at its midpoint is called a segment bisector.
Ex:
In the figure above, M is the midpoint of AB.
Plane N, MD, RM, and point M are all bisectors of AB.
We say that they bisect AB.
You can construct a line that bisects a segment without measuring to find the midpoint of the given segment.
Ex 9 The coordinates of the vertices of a quadrilateral are R (1 , 3) , S (3 , 3), T (5 , 1), and U (2 , 1). Find the perimeter of the quadrilateral. Round to the nearest tenth.