Pythagorean Theorem

222 hyplegleg

In a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.

222 cba (“c” is always the hypotenuse)

a

b

c

(leg)

(leg)

(hyp)

Distance Formula

212

212 yyxxd

Where d stands for distance

x1 & y1 are one endpoint of a segment

x2 & y2 are the second endpoint of a segment

(x1 , y1)

(x2 , y2)

d

What do you say when you walk into a cold room?

It’s collinear!

(It’s cold in here!)

Midpoint of a Segment

The point halfway between the endpoints of a segment

If X is the midpoint of Segment AB , then

ABXBAX

A

B

X

(the measure of AX = the measure of XB)

Midpoint Formula

On a Single Number Line:

On a Double Number Line (Coordinate

Plane):2

BAX

2 &

22121 yy

yxx

x

A B

-3 7

22

4

2

73

X

2

5 Units

5 Units

x

y(5,5)

(-3,-1)(x1,y1

)

(x2,y2

)

122

253 x 22

42

51 y

(1,2)

2

4020 M

2

baM

(a single number line)

102

20M

M

MPQM

2 &

22121 yy

yxx

x

(a double number line)

2

21 &

2

16

yx

5.12

3 & 2.5

2

5 yx

M(2.5, 1.5)

2) P(-1,

1) Q(6,

1.5) M(2.5,

(Not to scale)

Find the Coordinates of an Endpoint

The Midpoint Formula can be used to find the coordinates of an endpoint when the midpoint and one endpoint are given.Find the coordinates of Endpoint B, if M = 5 is the midpoint, and A = -12 is the other endpoint.

2

BAM

2

125

B Multiply both sides by 22 2

B 1210 Solve for B12 12

B22

A

-12 M

5 B

?22

17 units 17 units

(a single number line)

Let X = (x1,y1) (One endpoint)

Y = (-2, 2) (Midpoint)

Z = (2, 8) (Other endpoint)(x2, y2)

(x, y)

X(?)

Y(-2,2)

Z(2, 8)

(x, y)

(x2, y2)

(x1, y1)

(The midpoint is always the ordered

pair with no subscripts)

221 xx

x

2

22 1 x

2 2

24 1 x

16 x

2

82 1 y

221 yy

y

2 2

84 1 y

14 y

(-4, -6)

Look for an equation to write, then solve:

xx 21154 -2x-2x

1152 x

162 x+5+5

8x

Does it work?xx 21154

8211584 ?

1611532 ?

2727 Be sure to answer the question.

278211

211

xBC

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