Coordinate Geometry

Question 1

What are the different quadrants of the xy-plane?

Answer 1

Starting in the top right I, II, III, IV (going counter clockwise)

Question 2

How do you calculate the slope of a line?

Answer 2

Rise/run

Change in y / change in x

(Y2 - Y1) / (X2 - X1)

Question 3

Lines with positive slopes move in which direction and which quadrants must it intersect?

Answer 3

Upwards

Quadrants I and III

Question 4

What should you know about horizontal lines?

Answer 4

They have a slope of zero and the y coordinate is always the same.

Question 5

What should you know about vertical lines?

Answer 5

The have the same x coordinate and have an undefined slope.

Question 6

The larger the absolute value of a slope…

Answer 6

The steeper it is

Question 7

What is the slope intercept equation?

Answer 7

y=Mx + b

Where m is the slope, x is the corresponding x coordinate for the point on the line, y is the y coordinate for a point on the line and b is the y intercept of the line.

Question 8

At the x intercept, the value of y is what? And what is the coordinate pair?

Answer 8

0 and the coordinate pair is always (x,0)

Question 9

If you know the slope and y-intercept, what else do you also know?

Answer 9

The x intercept (-b/m)

Question 10

What is the equation of the x axis?

Answer 10

Y=0

Question 11

What is the equation of the y axis?

Answer 11

x=0

Question 12

What is the equation of a horizontal line?

Answer 12

y=b, where b is the y intercept

Question 13

What is the equation of a vertical line?

Answer 13

x=a where a is the x intercept of the line

Question 14

What is the standard form of an equation?

Answer 14

Ax + By = C

Where A,B, and C are constants.

Question 15

What info do you need to define a line?

Answer 15

1) a point on that line
2) the slope of that line or the slope of a line that is parallel or perpendicular to that line
3) another point on that line (eg x intercept, y intercept, or any other point)

Question 16

Parallel lines have:

Answer 16

The same slope but a different y intercept so they never intersect

Question 17

What must you know about perpendicular lines?

Answer 17

They intersect at 90 degrees and create 4 right angles. Their slopes are negative reciprocals of each other and multiply to -1

Question 18

How do you reflect point (x,y) over the x axis?

Answer 18

(x,-y)

Question 19

How do you reflect point (x,y) over the y axis?

Answer 19

(-x,y)

Question 20

How do you reflect point (x,y) over the origin?

Answer 20

(-x,-y)

Question 21

Reflection over the line y=x: what is the image when point (x,y) is reflected?

Answer 21

(y,x)

Question 22

Reflection over the line y=-x: what is the image when point (x,y) is reflected?

Answer 22

(-y,-x)

Question 23

Reflection over the line y=b: what is the image when point (x,y) is reflected?

Answer 23

(x,2b-y)

Question 24

Reflection over the line x=a: what is the image when point (x,y) is reflected?

Answer 24

(2a-x,y)

Question 25

How do you calculate the distance between 2 points using the distance formula?

Answer 25

Square root of:

(change in x)^2 + (change in y)^2

Question 26

When do you not have to use the distance formula when finding the distance between two coordinates and what do you do to find the distance instead?

Answer 26

When the two coordinates share the same x or y coordinate. Instead, you do the absolute value of the difference between the two distinct coordinates.

Question 27

How do you calculate the midpoint of a line segment?

Answer 27

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

Where (x1, y1) and (x2, y2) are the coordinates of the endpoints

Question 28

What is the equation of a circle centred at the point (a,b) with radius r?

Answer 28

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

Question 29

What is the equation of a circle centred at the origin/point (0,0) with radius r?

Answer 29

x^2 + y^2 = r^2

Question 30

Given two quadrilaterals with the same perimeter, which shape will always have the maximum area?

Answer 30

The square