1.4

1.4

How Can I Find It?Pg. 20

Midpoints and Constructions

1.4 – How Can I Find It? ______________Midpoints and Constructions

Today you are going to continue to develop your vocabulary for geometry as well as use your algebra knowledge. You will also use a straightedge and compass to explore different parts of shapes.

1.20 – MIDPOINT Segments have a point that can be found in the middle, called a midpoint. This stands for “middle point.” Examine the pictures below. Find the point in the middle of the segment.

M M

1.21 – MIDPOINT Sometimes the numbers are large. How can you find the midpoint of the following numbers?

a. 10 and 200

210 2

= 105

b. 32 and 66 c. 15 and 27

98 2

= 49 42 2

= 21

1.22 – MIDPOINTS ON GRAPHSFind the midpoint of segment AB. Look for any shortcuts that might help you.

A(5, 6)

M( , )

B(1, 2)

a. A(5, 6) and B(1, 2)

A

BM

3 4

A(-5, 6)

M( , )

B(3, -4)

b. A(-5, 6) and B(3, -4)

A

B

M-1 1

c. Without graphing, find the midpoint of

K(2, 125)

M( , )

L(98, 15)

50 70

d. Explain in your own words how to find the midpoint of a segment.

Add the x’s then divide by 2Add the y’s then divide by 2

It is the same…

f. Find the midpoint of A(-6, 2) and B(-2, -3).

(–6, 2)(–2, –3)–8 –1

(–4, –0.5)

___ ___ 2 2

1.23 – MIDPOINTS ON SEGMENTSGiven the midpoint, M, of the segment, find the indicated measures.

a.

x = _____________ XM = ___________ MZ = ___________ XZ = ___________

x + 2 = 2x – 3 2 = x – 3 5 = x5

5+2 = 7

2(5) – 3= 7

7+7 = 14

b.

x = _____________ PM = ___________ MR = ___________ PR = ___________

4x – 12 = -2x + 216x – 12 = 21

6x = 335.5

4(5.5)-12 = 10

-2(5.5)+21=10

10+10 = 20

x = 5.5

1.24 – FINDING AN ENDPOINTAs Cassie continued to work with her group, she started to think about a different situation. What if you knew the midpoint, but not the end of one side of the segment. Examine this with the problems below.

a. The midpoint (M) of segment AB is M(2, 1). If the coordinate of B is B(1, 4), what is the coordinate of the point A?

A( , )

M(2 , 1)

B(1, 4)

MB

A

3 –2

b. The midpoint (M) of segment AB is M(-1, -2). If the coordinate of A is A(4, 4), what is the coordinate of the point B?

A(4, 4)

M(-1, -2)

B( , )–6 –8

c. The midpoint (M) of segment AB is M(6, 5). If the coordinate of B is B(7, 8), what is the coordinate of the point A?

A( , )

M( 6, 5)

B( 7, 8)

5 2

d. The midpoint (M) of segment AB is M(1, 0). If the coordinate of A is A(-1, 2), what is the coordinate of the point B?

A( -1, 2)

M( 1, 0)

B( , )3 –2

1.25 – COPY A SEGMENTUsing a compass and straightedge, copy the segment. Do not erase any construction marks.

Copy a Segment: 1. Draw a ray that is longer than the original segment

2. Measure the segment with your compass

3. Put the point on the end of the ray and leave a mark with the pencil on the ray

4. Label the new point

a. Copy the segment.

'A 'B

'C 'D

E F

M

M

W X