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 :
Plot the points A(3, 5), B(3, -1) and C(-1, -3) on graph paper.
Join AB and BC.
From C draw a line CD parallel to AB, such that CD = AB.
From A draw a line AD parallel to BC, such that AD = BC.
Mark E, the mid-point of CD.
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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