## Coordinate Geometry Worksheet

Coordinate geometry refers to a branch of geometry that defines the position of a point on a plane. Furthermore, it uses a pair of numbers which we call coordinates. In addition, we will teach about the coordinate and Cartesian plane, slope formula, equation of the line, slopes of parallel lines, etc. You can download Coordinate Geometry Worksheet below –

**Coordinate and Cartesian Plane**

This is the basic concept of coordinate geometry. Also, it defines a 2-D plane in terms of perpendicular axes namely: x and y. Moreover, the x-axis specifies the horizontal direction while the y-axis depicts the vertical direction. Furthermore, it points their position along the x and y-axis in the coordinate plane.

Way to plot points and determine the coordinates of points on a coordinate plane?

Use a coordinate geometry worksheet and use two perpendicular lines called axes. Besides, the origin is the point at which the axes cross each other. And the arrows indicates the position direction of axes.

Take an ordered pair (2, 3). These number of ordered pair coordinates. In this, 2 is the coordinate on the x-axis and 3 is the coordinate on the y-axis.

**Slope of a line**

The slant line on a coordinate plane is the slope. Furthermore, it is the ration of the change in the y-value over the change in the x-value, which we know as rising over the sun. Besides, you can calculate the slope of a line by using this formula:

\( slope = \frac{change in y value}{change in x value} \)

Y-intercept

This is the point where the line meets the y-axis.

**Equation of a line**

This equation line can be written as:

y = mx + b

Here, m is the slope

b is the y-intercept

**Negative Slope**

A negative slope is a slope that touches the negative axis x or y.

**Slopes of parallel lines**

Two lines that are considered parallel if their slopes (m) are equal in coordinate geometry.

**Slopes of a perpendicular line**

These slopes are the perpendicular lines and are negative reciprocals of each other. In addition, means that if a line is perpendicular to a line that has a slope m, then the slope of the line is -1/m.

**Midpoint formula**

In some questions of coordinate geometry, you have to find the midpoint of a line segment on a coordinate plane. Furthermore, to find this point that is halfway amid two given points, get the average of the x-values and the average of the y-values.

However, the midpoint between two points ( \( x_{1},y_{1} \) ), and (\ ( x_{2}, y_{2} \) ) is

\( \left ( \frac{x_{1} + x_{2}}{2} , \frac{y_{1} + y_{2}}{2} \right ) \)

**Distance formula**

You can use the Pythagorean Theorem in a coordinate plane to find the distance between any two points. Besides, the distance between two points ( \( x_{1},y_{1} \) ), and ( \( x_{2}, y_{2} \) ) is

\( \sqrt {(x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{2}} \)

**Solved Example for you**

**Question:** Give step-wise details on how to plot two points (5, 3) on a coordinate geometry worksheet?

**Solution:** For graphing two points on a coordinate plane, we will use two perpendicular lines known as axes.

**Step-wise details**

- Firstly, draw two lines, one horizontal and other vertical. Moreover, make sure that they meet each other at the origin point.
- Now, mark the points on the x and y-axis equidistant from each other.
- Next, count the number 5 on the x-axis and search for 3 on the y-axis.
- After that, draw an imaginary line from point 5 and 3 and see where they interact.
- Lastly, the point at which these two-points meet is the point of intersection is the coordinate (5, 3).

Derivation of section formula in all four quadrants