Ch. 18 Coordinate Geometry

Question 1

Slope

Answer 1

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

Question 2

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

Answer 2

Steeper
Small abs value = flatter

Question 3

Slope-intercept equation

Answer 3

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

Question 4

How to determine x-intercept

Answer 4

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

Question 5

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

Answer 5

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

Question 6

Information needed to define a line

Answer 6

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

Question 7

Parellel line equations

Answer 7

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

Question 8

Perpendicular line equations

Answer 8

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

Question 9

Reflection over the x-axis

Answer 9

(x,y) –> (x, -y)

Question 10

Reflection over the y-axis

Answer 10

(x,y) –> (-x, y)

Question 11

Reflection over the origin

Answer 11

(x,y) –> (-x,-y)

Question 12

Reflection over the line y = x

Answer 12

(x,y) –> (y,x)

Question 13

Reflection over the line y = -x

Answer 13

(x,y) –> (-y,-x)

Question 14

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

Answer 14

(x,y) –> (x, 2b-y)

Question 15

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

Answer 15

(x,y) –> (2x-a, y)

Question 16

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

Answer 16

d = √(x2 - x1)^2 + (y2 - y1)^2

(can use pythagorean theorem to derive)

Question 17

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

Answer 17

Absolute value of the difference

Question 18

Midpoint formula

Answer 18

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

Midpoint is average of coordinates

Question 19

Equation for a circle in the coordinate plane

Answer 19

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)

Question 20

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

Answer 20

(x, y) –> (2a - x, 2b - y)