bell ringer camillus has two more than twice the points darius has. if camillus has 90 points, how...
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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!