Module 27: Coordinate Geometry

Question 1

Location of the 4 quadrants on the coordinate plane

Answer 1

In counter-clockwise order, starting in the top left, I, II, III, IV

Question 2

Calculating slope

Answer 2

Rise/run

OR

y2 - y1 / x2 - x1

Question 3

Slope of a hoirzontal line is _____; slope of a vertical line is ________

Answer 3

Zero; undefined

Question 4

Slope-Intercept Equation

Answer 4

y = mx + b

Question 5

Coordinate plane: Shortcut to find X & Y intercepts

Answer 5

Set X and Y equal to 0 in the original equation of y = mx+b.

y = -2x + 5
0 = -2x + 5
0 = -x + 5/2

x = 2.5
y = -2x + 5
y = -2(0) + 5
y = 5

Question 6

Calculating the x-intercept

Answer 6

1) Re-work the slope-intercept equation to isolate X.

y = mx +b
y - b = mx
x = (y - b) / m

2) Replace Y with 0

x = -b / m (b = Y intercept, m = slope)

Question 7

The equation for a vertical line is x = ____

Answer 7

the X intercept. Just one number.

Same idea for a horizontal line: Y = 4 (if the y-intercept is 4)

Question 8

How to determine if a point is on a line, when the slope-intercept equation of the line is given

Answer 8

1) Insert the x & y values of the point into the slope-intercept equation that was given.
2) Simplify
3) If the statement is true, the point is on the line. If it’s false, the point is not on the line

Question 9

In order to define a line’s equation, you must know one point on the line as well as (2 options:)

Answer 9

• the slope of the line (or a slope of a line that is parallel/perpendicular)
• a second point on the line, to then use rise/run to find the slope

Question 10

How to calculate distance between two points

Answer 10

Pythagorean theorem!

• Graph the line, draw legs of a right triangle below it.
• Vertical leg = rise, horizontal leg = run
• (rise)^2 + (run)^2 = c^2

Question 11

The product of the slope of two perpendicular lines

Answer 11

-1 (always, because they are negative reciprocals)

For example: 2 and - 1/2

Question 12

Coordinates of an x-axis reflection

Answer 12

(x,y) -> (x,-y)

The Y value gets flipped

Question 13

Coordinates of a y-axis reflection

Answer 13

(x,y) -> (-x,y)

The X value gets flipped

Question 14

Coordinates of a reflection over the origin

Answer 14

(x,y) -> (-x,-y)

Both points get flipped

Question 15

Reflecting a line, steps

Answer 15

1) Pick any 2 points on the line (start with the Y intercept and 1-2 spots away from it - easiest)
2) Reflect the 2 points over the line axis. Re-calc the slope for these points if need be
* Note: Reflections are not necessarily perpendicular

Question 16

When calculating slope, I will

Answer 16

be careful not to lose a negative sign in the rise/run equation. Subtracting a negative number = a positive number. (Made this mistake a few times in practice)

Question 17

Formula for the midpoint of a line

Answer 17

(x1+x2)/2, (y1+y2)/2

Take the average of each coordinate

Question 18

When I see an inequality involving a coordinate plane, I will

Answer 18

make sure the inequality is in slope/intercept form, with the Y isolated on one side, before solving.

Question 19

Does a point support a given inequality? How to test

Answer 19

Plug the (x,y) coordinates into the equation of the threshold of the inequality; see if the inequality statement is true or false.