Chapter 1.3-1.4 Midpoint Formula Construct Midpoints.
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Transcript of Chapter 1.3-1.4 Midpoint Formula Construct Midpoints.
Chapter 1.3-1.4
Midpoint FormulaConstruct Midpoints
• Midpoint (of a segment) – the point that splits the segment into 2 equal parts (where the segment is cut)
• If X is the midpoint of AC and XC = 10, how long is AX? AC?
A Z B
With AlgebraZ is midpoint of MP. Find x.
M Z P
3x 24 - x
3x = 24 – x
+1x= + 1x
4x = 24
X = 6
Bisector (of a segment) – a line, segment ray, or plane that intersects a segment at the midpoint (it does the cutting)
A Z B
mbisector
midpoint
Hatch Marks – short slash markings that show two or more segments are equal in length
W X Y Z
WX = YZ
Congruent - segments that have the same measure (like equal)
~
Urkle Stephon
Zack Cody
2 1midpoint2
x xx
2 1
midpoint2
y yy
midpoint midpoint( , )x y
Midpoint formula:
2 1midpoint2
x xx
2 1midpoint2
y yy
midpoint midpoint( , )x y
Find the midpoint whose endpoints are (2, -3) and (-14, 13)1, 1( )x y 2, 2( )x y
14 2
212
6
( , )6
13 3
210
5
5
+
2= y midpoint
+
2= x midpoint
2 1midpoint2
x xx
2 1midpoint2
y yy
midpoint midpoint( , )x y
Find the midpoint whose endpoints are (1, -2) and (-17, 16)1, 1( )x y 2, 2( )x y
17 1
216
8
( , )8
16 2
214
7
7
+
2= x midpoint
+
2= y midpoint
What if you are missing an endpoint ?
• When given the midpoint and one endpoint, set up the formula just as before.
(-2,2) (-3,-5)
( ?, ?)
M(-3, -5) is the midpoint of RS. If S has a coordinates
(-2, 2), find the coordinates of R.
2, 2( )x y
2
12 x 6
( , )4
2 1y
12
,( )m mx y
(x1, y1) (-2, 2)M(-3, -5)
3 5(2) (2)
2 2
1x 4
(2) (2)
12 y 102 2
1y 12
R S
+
2= +
2=
(x1, y1)
x1 y1
M(4, 2) is the midpoint of RS. If S has a coordinates (5, -2), find the coordinates of R.
2, 2( )x y
5
15 x 8
( , )3
2
6
,( )m mx y
R (x1, y1) S (5,-2)M(4, 2)
4 2(2) (2)
5 5
1x 3
(2) (2)
12 y 42 2
1y 6
+
2= +
2=
x1 y1
(x1, y1)
Book p.41-44
The End!