Problem 11 - Precalculus Essentials

Question

Plot the given point in a rectangular coordinate system. $$\left(\frac{7}{2},-\frac{3}{2}\right)$$

Step-by-Step Solution

Answer

The point \(\left(\frac{7}{2},-\frac{3}{2}\right)\) is found in the fourth quadrant, 3.5 units to the right of the vertical axis (y-axis) and 1.5 units below the horizontal axis (x-axis).

Step 1: Understand the Cartesian coordinate system

A Cartesian coordinate system represents each point in the plane by an ordered pair \((x, y)\), where 'x' is the abscissa (horizontal coordinate) and 'y' is the ordinate (vertical coordinate). The 'x' value (abscissa) represents the horizontal distance of the point from the origin (either to the right (+) or the left (-)), and the 'y' value (ordinate) represents the vertical distance from the origin (either upwards (+) or downwards (-)).

Step 2: Decoding the given point

The given point \(\left(\frac{7}{2},-\frac{3}{2}\right)\) can be read as 'x' is half of 7 (which is 3.5) and 'y' is negative half of 3 (which is -1.5). This means we move 3.5 units to the right and 1.5 units down from the origin (0,0).

Step 3: Plot the point

Plot the point (3.5, -1.5). Start at the origin, move 3.5 units to the right and from there move 1.5 units down. Mark this point.