Question

The point (a, b) is in Quadrant II of a coordinate plane. Describe the location of the point with the given coordinates.

$(\text{a,} \text{a})$

Short answer

The location of the point $\left(a,a\right)$is $a$ units left to the origin and then $a$units up from the $x$-axis.

Step-by-step solution

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

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

Step 3: The point (a, b) is in Quadrant II of a coordinate plane. Describe the location of the point with the given coordinates.

Consider, the point provided in the question: $\left(a,a\right)$

Since the point $\left(a,a\right)$is in Quadrant II. Therefore, point$\left(a,a\right)$ is $a$ units left to the origin and then$a$units up from the $x$-axis.

Thus, the location of the point$\left(a,a\right)$ is$a$units left to the origin and then $a$units up from the $x$-axis.