Coordinate Geometry Calculator

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Example

Created on 2024-06-20Asked by Ella Martin (Solvelet student)

Find the distance between the points

P(3, 4)

and

Q(-2, -1)

Solution

Step 1: Identify the coordinates of points

P(3, 4)

and

Q(-2, -1)

. Step 2: Use the distance formula:

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

Step 3: Substitute the coordinates:

d = \sqrt{(-2 - 3)^2 + (-1 - 4)^2}.

Step 4: Compute the distance:

d = \sqrt{(-5)^2 + (-5)^2} = \sqrt{50}.

Step 5: Simplify the square root:

d = \sqrt{25 \cdot 2} = 5\sqrt{2}.

Step 6: Conclusion. The distance between points

P(3, 4)

and

Q(-2, -1)

5\sqrt{2}

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Jacob Young on Solvelet

1. Find the distance coordinate plane

(3, 4)

and

(-1, 2)

2. Determine the equation of the line passing through the points

(1, 2)

and

(4, 5)

DefinitionCoordinate geometry is a type of applied geometry that uses the coordinate spaces to study the properties and characteristics of geometric elements. The concept of coordinate geometry abstracts from the concrete definition of points, straight lines, or curves the notion of their coordinates and equations. It is mainly used to study the properties of algebraic geometrizations of figures when considering an n -dimensional space or a plane. This topic is widely used in such areas as mathematics, physics, engineering, or computer graphics. For example, an equation for a circle with a given center and radius r in a Cartesian coordinate system is given by the formula.

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