Question

Point O is the origin of a coordinate plane. Choose points $\text{P,} \text{Q,} \text{and} \text{R} \text{so} \text{that} \text{O,} \text{P,} \text{Q,} \text{and} \text{R}$are the corners of a square with a side length of 5 units. Identify the coordinates of $\text{P,} \text{Q,} \text{and} \text{R}$. Explain your reasoning.

Short answer

The point coordinate of the point $P$, $Q$and $R$ are $\left(5,\text{0}\right)$,$\left(5,5\right)$and$\left(0,\text{5}\right)$ respectively.

Step-by-step solution

Step 1. What is a coordinate system? 

A Rectangular or Cartesian coordinate system in two dimensions (x and y) is defined by an ordered pair of perpendicular lines or axes.

Points are placed by their distance along a horizontal (x) and vertical (y) axis from the origin, defined as (0, 0).

Coordinate of the Origin

It has zero distance from both the axes. Hence the coordinates of the origin are (0, 0).

Sign convention of all quadrants:

First quadrant: x – positive and y – positive

2^nd quadrant: x – negative and y – positive

3^rd quadrant: x – negative and y – negative

4^th quadrant: x – positive and y – negative

Step 2. Coordinate Geometry in Two Dimensional Plane

Incoordinate geometry, first, we learn about locating the points in a X – Y coordinate plane.

For example, the point (2, 3) is 3 units away from the X−axis measured along the positive X−axis and 2 units away from Y−axis measured along the positive Y−axis.

The points having x-coordinate as ‘0′ lies on the Y−axis and the points having Y-coordinate as ‘0’ lies on the X−axis

For example, the points (2, 0), (5, 0) lies on X−axis and the points (0, −3), (0, 7) lies on Y−axis

Choose points P, Q, and R so that O, P, Q, and R are the corners of a square with a side length of 5 units. Identify the coordinates of P, Q, and R. Explain your reasoning.

Consider, the statement provided in the question,

Point $O$is the origin of a coordinate plane.

Since, $O$, $P$, $Q$and $R$are the corners of the square with the side length of 5 units.

Thus, the point coordinate of the point $P$, $Q$and $R$are $\left(5,\text{0}\right)$, $\left(5,5\right)$and $\left(0,\text{5}\right)$ respectively.