The Coordinate Plane
The coordinate plane is a two-dimensional number line that we use for graphing, for representing relationships between quantities.
The Coordinate Plane
The coordinate plane has a horizontal number line called the \(x\)-axis and a vertical number line called the \(y\)-axis. The point at which the lines intersect is called the origin.
A jumping frog is starting at the origin. He can move either vertically or horizontally only one unit at a time. How many possible points can he land on after 2 jumps?
The graph below shows all of the locations where the frog can land. There are 8 possible options.
Which of these students scored higher on the final than on the midterm?
The dashed line represents scenarios of having equal scores on the final and midterm.
The points above the dashed line have a higher final score than midterm score. The only one of the four students whose point is above the dashed line is Zoe, who scored a 77 on the midterm and an 87 on the final.
Graphing Coordinates
Every point has a set of coordinates, \((x,y),\) that describe its location on the coordinate plane.
The first number in parentheses is the \(x\)-coordinate and the second number is the \(y\)-coordinate. The origin has the coordinates \((0,0).\) The point \((2,3)\) is located at 2 along the \(x\)-axis and 3 along the \(y\)-axis. We can also think of the point \((2,3)\) being 2 units to the right of the origin and 3 units up from the origin.
What are the coordinates of the blue point and the orange point?
The blue point is right 4 and down 2 from the origin, so its coordinates are \((4,-2).\) The orange point is left 1 and up 3 from the origin, so its coordinates are \((-1,3).\)
Where could you add a fourth point to make a square?
The four side lengths on a square are equal. Therefore, opposite sides of the square must each be the hypotenuse of the same size right triangles.
To get from the point \((3,-1)\) to \((-1,-3),\) we need to move down 2 units and left 4 units.
If we move left 4 units and down 2 units from the upper point of \((1,3),\) we end up at \((-3,1),\) and have our square.
Quadrants
The intersection of the \(x\)-axis and \(y\)-axis divides the coordinate plane into four quadrants.
In which quadrant does the point \((5,-7)\) lie?
The \(x\)-coordinate is positive and the \(y\)-coordinate is negative so the point lies in the fourth quadrant.