Find the area of the triangle formed by the following points (3, 1), (5,0), (1,2) (iii) (-1.5,3), (6,2), (-3, 4) What do you observe? Plot these points three different graphs. What do you observe? Can we draw a triangle having area zero square units ? What does it mean?
Answers
Answer:
if vertices of triangles are (x_1,y_1),(x_2,y_2)(x1,y1),(x2,y2) and (x_3,y_3)(x3,y3) then, area of triangle =\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|21∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣
(i) (2,0), (1,2) , (1,6)
area of triangle = 1/2 |2(2 - 6) + 1(6 - 0) + 1(0 - 2)|
= 1/2|2 × -4 + 1 × 6 + 1 × -2 |
= 1/2|-8 + 6 - 2|
= 1/2 |-4|
= 1/2 × 4
= 2 sq unit
(ii) (3,1) , (5,0) , (1,2)
area of triangle = 1/2|3(0 - 2) + 5(2 - 1) + 1(2 - 1)|
= 1/2| 3 × -2 + 5 × 1 + 1 × 1 |
= 1/2 | -6 + 5 + 1 |
= 1/2 | -6 + 6|
= 1/2 × 0 = 0
e.g., area of triangle = 0
means givens points are collinear.
(iii) (-1.5, 3) , (6,2) and (-3,4)
area of triangle= 1/2|-1.5(2 - 4) + 6(4 - 3) -3(3 - 2)|
= 1/2| -1.5 × -2 + 6 × 1 - 3 × 1 |
= 1/2 | 3 + 6 - 3 |
= 1/2 | 6 |
= 1/2 × 6 = 3 sq unit