Bell RingerCamillus has two more than twice the points Darius has. If Camillus has 90 points, how many does Darius have?

2d + 2 = 90 – 2 – 2

2d = 88 d = 44 points

Quiz Answers…

a. (-8, 1)b. (-2, 4)c. (1, 3)d. (0, -7)e. (3, -4)

1. 2.

3. m = 3 4. m = -9/16 5. m = -76. m = -37. m = 0

x y0 -61 -22 2

x y0 11 02 -1

Quiz Answers…

8. m = 2 b = -6y = 2x – 6

9. y = 4x + 210. y = 411. y = -3x – 1

12. b = -10y = 3x – 10 13. b = 10y = -2x + 1014. m = 4, b = 13 y = 4x + 1315. m = -2, b = 5 y = -2x + 5

Quiz Answers…

Extra Credit:a.y = ¼ x – ¼b.y = -3x + 6

The Midpoint FormulaGRE 504: Find the midpoint of a line segment*

What we know…The midpoint is the middle of a line segment.

We will find the middle of horizontal and vertical lines first.

Vertical and Horizontal Lines

Find the midpoint by dividing the line segment by two.

.(-8, 7) (2, 7)(-3, 7)

Here’s the midpoint

(6, -1)

(6, -8)

(6, 6)

.

Here’s the midpoint

Diagonal Lines!!!! Noooooo!!!

The Midpoint…

.(-1, 0)

(3, 6)

(-5, -6)

Here’s the middle of

yFind the middle of the x and y.

12

8 Here’s the middle of

x

Here’s the midpoint!

So, we just add the x’s

and divide by 2 and we add the y’s and divide by 2.

The Midpoint Formula

x1 + x2 y1 + y2

2 2( ),Where (x1, y1) and (x2, y2) are the

endpoints of the line segment.

(3, 6) (9, 2)(x1, y1) (x2, y2)

The Midpoint Formulax1 + x2 y1 + y2

2 2( ),

(3, 6) (9, 2)3 + 9 6 + 2

2 2 12 8 2 2

,( ),( )= (6,

4)

The answer could be in fractions!