Ch. 18 Coordinate Geometry Flashcards

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1
Q

Slope

A

m = (Y2 - Y1) / (X2 - X1)

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2
Q

The greater the absolute value, the ____ (steeper/ flatter) the slope is.

A

Steeper
Small abs value = flatter

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3
Q

Slope-intercept equation

A

y = mx + b
y – y coordinate
m – slope
x – x coordinate
b – y-intercept

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4
Q

How to determine x-intercept

A

Use y = mx + b
Make y = 0, solve for x.
(when y is 0, that’s where the line will intercept the x-axis)

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5
Q

How to determine if point A(x,y) is on a certain line.

A

Plug coordinates x & y from Point A into the equation: y = mx+b
If it’s still equal, then the point is on the line

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6
Q

Information needed to define a line

A

y = mx+b
1. One point on the line AND
2. Slope of the line (or slope of a line that’s parallel or perpendicular to the line)
OR
2. A second point on the line (y-int, x-int, or any other point) - to determine the slope

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7
Q

Parellel line equations

A

Same slope, different y-int
same m; different b
y = 4x + 3
y = 4x - 1/2

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8
Q

Perpendicular line equations

A

The product of their slopes is -1
(Their slopes are negative reciprocals)

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9
Q

Reflection over the x-axis

A

(x,y) –> (x, -y)

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10
Q

Reflection over the y-axis

A

(x,y) –> (-x, y)

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11
Q

Reflection over the origin

A

(x,y) –> (-x,-y)

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12
Q

Reflection over the line y = x

A

(x,y) –> (y,x)

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13
Q

Reflection over the line y = -x

A

(x,y) –> (-y,-x)

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14
Q

Reflection over the line y = b where b is any constant

A

(x,y) –> (x, 2b-y)

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15
Q

Reflection over the line x = a where a is any constant

A

(x,y) –> (2x-a, y)

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16
Q

Distance between two points (x1, y1) and (x2, y2)

A

d = √(x2 - x1)^2 + (y2 - y1)^2

(can use pythagorean theorem to derive)

17
Q

If two points have the same x- or y- coordinates, how do you calc distance?

A

Absolute value of the difference

18
Q

Midpoint formula

A

xm, ym = (x1+x2) / 2 , (y1 + y2) / 2

Midpoint is average of coordinates

19
Q

Equation for a circle in the coordinate plane

A

Let (a,b) be the center of the circle & r be the radius:

(x - a)^2 + (y - b)^2 = r^2

(can use distance formula to derive, let (x, y) be any point on the circle)

20
Q

When we reflect points (x,y) over point (a,b), (x,y) becomes what?

A

(x, y) –> (2a - x, 2b - y)