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# Coordinate Geometry Formulas

The list of all coordinate geometry formulas for classes 9, 10, and 11 is provided here to help the students. To recall, coordinate geometry is the study of geometry using the coordinate points. In coordinate geometry, the position of a point can be easily defined using coordinates.

## Coordinate Geometry Formulas List for Classes 9, 10 and 11

Coordinate geometry is an integral topic in classes 9, 10 and 11. All the important coordinate geometry formulas for class 9, class 10 and class 11 are given below.

All Formulas of Coordinate Geometry
General Form of a Line Ax + By + C = 0
Slope Intercept Form of a Line y = mx + c
Point-Slope Form y − y1= m(x − x1)
The slope of a Line Using Coordinates m = Δy/Δx = (y2 − y1)/(x2 − x1)
The slope of a Line Using General Equation m = −(A/B)
Intercept-Intercept Form x/a + y/b = 1
Distance Formula |P1P2| = √[(x2 − x1)2 + (y2 − y1)2]
For Parallel Lines, m1 = m2
For Perpendicular Lines, m1m2 = -1
Midpoint Formula M (x, y) = [½(x1 + x2), ½(y1 + y2)]
Angle Formula tan θ = [(m1 – m2)/ 1 + m1m2]
Area of a Triangle Formula ½ |x1(y2−y3)+x2(y3–y1)+x3(y1–y2)|
Distance from a Point to a Line d = [|Ax0 + By0 + C| / √(A2 + B2)]
Section Formula (Internal division) P(x, y) = [(m1x2 + m2x1)/(m1 + m2), (m1y2 + m2y1)/(m1 + m2)]
Section Formula (External division) P(x, y) = [(m1x2 – m2x1)/(m1 – m2), (m1y2 – m2y1)/(m1 – m2)]

## Solved Examples

Example 1:

What is the slope of the line joining the points P(-2, 3) and Q(2, 7)?

Solution:

Let the given points be:

P(-2, 3) = (x1, y1)

Q(2, 7) = (x2, y2)

Solpe of the line PQ = (y2 – y1)/(x2 – x1)

= (7 – 3)/ [2 – (-2)]

= 4/4

= 1

Example 2:

If the distance between the points A(2, –2) and B(–1, x) is 5, find the value of x.

Solution:

Let the given points be:

A(2, -2) = (x1, y1)

B(-1, x) = (x2, y2)

Distance between A and B = √[(x2 – x1)2 + (y2 – y1)2]

√[(-1 – 2)2 + (x + 2)2] = 5 [given distance is 5]

Squaring on both sides, we get;

(3)2 + (x + 2)2 = 25

(x + 2)2 = 25 – 9

(x + 2)2 = 16

x + 2 = ± 4

When x + 2 = 4, x = 2

When x + 2 = -4, x = -6

### Practice Questions Using Coordinate Geometry Formulas

1. Find the distance between two points (1, -2) and (-3, 5). (Hint: Distance Formula)
2. Calculate the slope of a line with coordinates (2,7) and (8,1). (Hint: Slope Formula)
3. Calculate the area of a triangle ∆ABC whose vertices are at A(1,2), B(4,2) and C(3,5). (Hint: Area Of A Triangle In Coordinate Geometry)
4. Calculate the midpoint of the line segment joining the points P(4, 5) and Q(6, 7) (Hint: Midpoint Formula)

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## Frequently Asked Questions – FAQs

### What is the formula for the slope of a line joining two points in coordinate geometry?

In coordinate geometry, the slope of a line joining two points (x1, y1) and (x2, y2) is m = (y2 – y1)/(x2 – x1)

### What is the distance formula in coordinate geometry?

The distance formula in coordinate geometry is given by:
D = √[(x2 – x1)2 + (y2 – y1)2]

### Write the midpoint formula in coordinate geometry.

In coordinate geometry, the midpoint formula is given as:
[(x1 + x2)/2, (y1 + y2)/2]
Quiz on Coordinate Geometry Formulas