The Coordinate Plane — Challenge
Two numbers pin down any point, once you agree which one comes first.
What these problems cover
These questions use 5 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Mean — Two kinds of centre: the balance point, and the middle value.
- Origin — The point (0, 0), which every proportional graph passes through.
- Perimeter — Distance all the way around the outside.
- Area — Space inside, measured in square units.
- Quadrant — One of the four regions the axes divide the plane into.
Problem 1
In which quadrant does the point (-4,7) lie?
- I
- II
- III
- IV
- On an axis
Worked answer
II
Quadrant I has both coordinates positive, and the numbering runs anticlockwise from there.
Here x is negative and y is positive, which is the top left.
That is quadrant II.
Problem 2
What are the coordinates of (3,5) after reflection in the x-axis?
- (3,-5)
- (-3,5)
- (-3,-5)
- (5,3)
- (3,5)
Worked answer
(3,-5)
Reflecting in the x-axis flips the point above or below that line, so the sign of y changes and x stays put.
(3,5) becomes (3,-5).
Reflecting in the y-axis instead would give (-3,5).
Problem 3
What are the coordinates of the origin?
- (0,0)
- (1,1)
- (0,1)
- (1,0)
- (-1,-1)
Worked answer
(0,0)
The origin is where the two axes cross, so no movement has been made in either direction.
Both coordinates are therefore zero: (0,0).
Problem 4
In the point (4,-6), what is the y-coordinate?
- 4
- -6
- 6
- -4
- 10
Worked answer
-6
Coordinates are always written as (x,y), with the horizontal value first.
So the second number, -6, is the y-coordinate.
Problem 5
In which quadrant does the point (5,2) lie?
- I
- II
- III
- IV
- On an axis
Worked answer
I
Both coordinates are positive, so the point is right of the vertical axis and above the horizontal one.
That is the top right, which is quadrant I.
Problem 6
The point (-3,0) lies where?
- On the x-axis
- On the y-axis
- In quadrant II
- In quadrant III
- At the origin
Worked answer
On the x-axis
A y-coordinate of 0 means no movement up or down from the origin.
The point therefore sits on the horizontal axis, which is the x-axis, three units to the left.
Problem 7
In which quadrant does the point (-2,-8) lie?
- I
- II
- III
- IV
- On an axis
Worked answer
III
Both coordinates are negative, so the point is left of the vertical axis and below the horizontal one.
That is the bottom left, which is quadrant III.
Problem 8
What is the distance between (1,3) and (1,9)?
- 2
- 4
- 6
- 8
- 10
Worked answer
6
The two points share the same x value, so the segment joining them is vertical.
The distance is just the difference in the y values: 9-3 = 6.
No square roots are needed when the segment runs along one direction only.