MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade:
        The vertices of a triangle ABC are (3,0) (0,6)&(6,9). The line DE divides AB and AC in the ratio of 1:2.prove that∆ABC=9∆ADE.
2 years ago

Answers : (1)

Arun
23832 Points
							

Dear Student

 

By question D divides AB internally in the ratio 1 : 2; hence, the co-ordinates of D are ((1 ∙ 0 + 2 ∙ 3)/(1 + 2), (1 ∙ 6 + 2 ∙ 0)/(1 + 2)) = (6/3, 6/3) = (2, 2). 

Again, E divides AC internally in the ratio 1 : 2; hence, the co-ordinates of E are 

((1 ∙ 6 + 2 ∙ 3)/(1 + 2), (1 ∙ 9 + 2 ∙ 0)/(1 + 2)) = (12/3, 9/3) = (4, 3). 

Now, the area of the triangle ABC

= ½ |(18 + 0 + 0) - (0 + 36 + 27)| sq. units. 

= ½ |18 - 63| sq. units. 

= 45/2 sq. units. 

And the area of the triangle ADE 

= ½ |( 6 + 6 + 0) - (0 + 8 + 9)| sq. units. 

= ½ |12 - 17| sq. units.

= 5/2 sq. units. 

therefore, area of the ∆ ABC 

= 45/2 sq. units = 9 ∙ 5/2 sq. units. 

= 9 ∙ area of the ∆ ADE. Proved
 

Regards

Arun (askIITians forum expert)

2 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details