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.
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Which of these students scored higher on the final than on the midterm?
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The dashed line represents scenarios of having equal scores on the final and midterm.
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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?
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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?
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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.
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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.
In what quadrant is the point \( (-1,-11) \)?
Details and assumptions
Quadrant I should be entered as "1", Quadrant II should be entered "2", etc.