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Mathematics

Three vertices of a parallelogram are A(3, 5), B(3, -1) and C(-1, -3). Plot these points on a graph paper and hence use it to find the coordinates of the fourth vertex D. Also find the coordinates of the mid-point of the side CD. What is the area of the parallelogram?

Coordinate Geometry

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Answer

Steps of construction :

  1. Plot the points A(3, 5), B(3, -1) and C(-1, -3) on graph paper.

  2. Join AB and BC.

  3. From C draw a line CD parallel to AB, such that CD = AB.

  4. From A draw a line AD parallel to BC, such that AD = BC.

  5. Mark E, the mid-point of CD.

Three vertices of a parallelogram are A(3, 5), B(3, -1) and C(-1, -3). Plot these points on a graph paper and hence use it to find the coordinates of the fourth vertex D. Also find the coordinates of the mid-point of the side CD. What is the area of the parallelogram? Coordinate Geometry, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

From graph,

The coordinates of fourth vertex D are (-1, 3).

The coordinates of the midpoint of CD i.e. E are (-1, 0).

As, 1 block = 1 unit

EF = 4 units

CD = 6 units

Area of parallelogram ABCD = Base × height

= CD × EF

= 6 × 4

= 24 sq. units.

Hence, D = (-1, 3), coordinates of mid-point of CD = (-1, 0) and the area of the parallelogram is 24 sq. units.

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