29. If A (0,5), B(6, 11 ) and C(10,7) are the vertices of a 4 ABC, D and E
are the mid-points of AB and AC respectively. Then find the area of A ADE.
Answers
The area of ΔADE is 6 square units.
Step-by-step explanation:
The coordinates of the vertices A, B, C are (0, 5), (6, 11), (10, 7) respectively.
Since D, E are the mid-points of AB, AC respectively, the coordinates of D, E be
( (0 + 6)/2, (5 + 11)/2 ), ( (0 + 10)/2, (5 + 7)/2 ) respectively
i.e., (6/2, 16/2), (10/2, 12/2) respectively
i.e., (3, 8), (5, 6) respectively.
We have to find the area of ΔADE whose vertices are A (0, 5), D (3, 8) and E (5, 6).
Using the determinant formula to find the area of a triangle in 2D-coordinate geometry, we get the area of ΔADE
| 0 5 1 |
= 1/2 * | 3 8 1 | square units
| 5 6 1 |
= 1/2 * [ 0 - 5 (3 - 5) + 1 (18 - 40) ] square units
[ expanding along the first row ]
= 1/2 * [ 0 + 10 - 22 ] square units
= 1/2 * [ - 12 ] square units
= 6 square units [ taking the modulus value ]
Related question:
Find the area of triangle formed by the points A (2, 0), B (6, 0) and C (4, 6). - https://brainly.in/question/3179572
