Question

Use the coordinate plane in Example 1.

Give the coordinates of the point.

1. C

Short answer

The coordinate of the point C is $\left(4,2\right)$.

Step-by-step solution

What is a coordinate system? 

A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis.

Points are designated by their distance along a horizontal (x) and vertical (y) axis from a reference point, the origin, designated (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 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: Give the coordinates of the point.

Consider, the coordinate plane provided in the question,

From, the graph provided in the question, it can be easily observed that point C is 4 units to the right of the origin and 2 units up.

Thus, the $x$co-ordinate is 4, and the $y$-coordinate is 2.

The coordinate of the point C is $\left(4,2\right)$.