Math's: Coordinate System: Plotting of a Point and Distance Between Two Points

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Plotting of a Point Whose Coordinates Are Given

The point can be plotted by measuring its distances from the axes.

Thus, any point can be plotted as follows:

  • Measure equal to h along the x-axis

  • Measure perpendicular to and equal to .

Plotting of a Point

Plotting of a Point

Distance between Two Points

The distance of the line segment joining two points whose coordinates are and is given by,

Distance Between Two Points

Distance between Two Points

The distance between any two points and in the plane is the length of the line segment .

Since is a right triangle,

Section Formula

Section Formula

Section Formula

The co-ordinates of a point which divides the line segment joining the points and in the ratio internally are-

The co-ordinates of the mid-point of the line segment joining two points and can be obtained by taking in the section formula above. Thus, the co-ordinates of the mid-point joining two points and are:

Centroid of a Triangle

The centroid of a triangle is the point of concurrency of its medians and divides each median in the ratio of .

Centroid of a Triangle

Centroid of a Triangle

The co-ordinates of the centroid of a triangle whose vertices and are given by-

1. Find the centroid of the triangle whose vertices are and

Solution- The coordinates of the centroid of a triangle

coordinates of the centroid-

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