Question
Download Solution PDFComprehension
Direction: Consider the following for the next two (02) items that follow.
The coordinates of three consecutive vertices of a parallelogram ABCD are A(1, 3), B(-1, 2) and C(3, 5).
What is the area of the parallelogram?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The diagonal of a parallelogram divides it into two parts of equal areas.
Area of triangle having three coordinates (x1, y1), (x2, y2), (x3, y3)
Area = (1/2) | [x1 (y2 – y3 ) + x2 (y3 – y1 ) + x3(y1 – y2)] |
Calculation:
Here in the figure diagonal AC divides ABCD into two equal parts
Area(ABCD) = 2 × Area (ΔABC) ----(i)
Area (ΔABC) = (1/2) | [1 (2 - 5) + (-1) (5 - 3) + 3 (3 - 2)] |
⇒ Area (ΔABC) = (1/2) | [ -3 - 2 + 3 ] |
⇒ Area (ΔABC) = (1/2) | - 2 | = 1
Now, From (i), we get
Area(ABCD) = 2 × 1 = 2
∴ The area of parallelogram is 2 square unit.
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