Question

The point that is 3 units to the right of the y-axis and 5 units below the x-axis has coordinates$\left(\text{\_\_\_\_,\_\_\_}\right)$.

Short answer

The point that is 3 units to the right of the y-axis and 5 units below the x-axis has coordinates $\left(3,-5\right)$.

Step-by-step solution

Step 1. Apply the concept of the Cartesian Plane.

The Cartesian plane is divided into four quadrants. Numbers on the right of zero are positive, on the left of zero are negative. Numbers above zero on the vertical line are positive and numbers below 0 are negative. Each pair of points in the coordinate plane is represented as an ordered pair$\left(x,y\right)$ where the first element is the x-coordinate and the second element is the y-coordinate. The point$\left(x,y\right)$ denotes it is x units on thex-axis and y units on they-axisand marked accordingly.

Step 2. Apply the concept of Quadrants.

The Cartesian plane is divided into four quadrants.

The coordinates in Quadrant I are of the form $\left(x,y\right)$where both x and y are positive.

The coordinates in Quadrant II are of the form$\left(-x,y\right)$ where x is negative and y is positive.

The coordinates in Quadrant III are of the form$\left(-x,-y\right)$ where x and y are negative.

The coordinates in Quadrant IV are of the form$\left(x,-y\right)$ where x is positive and y is negative.

Step 3. Compute the coordinates. 

Consider the provided information about the coordinates.

The point is 5 units below the x-axis so, its y-coordinates are negative.

The point is 3 units to the right of the y-axis so, its x-coordinate is positive.

From the interpretation, the point lies in the fourth quadrant.

Therefore, the coordinates of the point are $\left(3,-5\right)$.

Hence, the point that is 3 units to the right of the y-axis and 5 units below the x-axis has coordinates $\left(3,-5\right)$.