Problem 12 - Precalculus Essentials

Question

Plot the given point in a rectangular coordinate system. $$\left(-\frac{5}{2}, \frac{3}{2}\right)$$

Step-by-Step Solution

Answer

The point \(-5/2, 3/2\) can be plotted in the second quadrant of the rectangular coordinate system after moving 2.5 units to the left of the origin and 1.5 units upwards.

Step 1: Understand the Coordinate System

A rectangular (or Cartesian) coordinate system is divided into four quadrants by two perpendicular lines called axes. The horizontal axis is called the x-axis, and the vertical axis is called the y-axis. The point where the axes intersect is the origin, and it has coordinates (0,0). The position of any point on the plane is given by an ordered pair of numbers (x, y). The x-coordinate represents horizontal displacement from the origin (positive to the right, negative to the left), and the y-coordinate represents vertical displacement (positive upwards, negative downwards).

Step 2: Understand the Given Coordinates

The given point is \(-5/2, 3/2\) (or -2.5, 1.5 in decimal form). The negative x-coordinate tells us the point is to the left of the origin, and the positive y-coordinate tells us the point is above the origin.

Step 3: Plot the Point

To plot the point, move 2.5 units to the left from the origin on the x-axis (since x-coordinate is -2.5) then move 1.5 units upwards on the y-axis (since y-coordinate is positive 1.5). That's the point \(-5/2, 3/2\) on the coordinate plane.