solve ques in the attachment
Coordinate Geometry
Answers
Answer:
Area of ΔADE = (1/9) * Area of ΔABC
Step-by-step explanation:
Given vertices are A(4,6), B(1,5) and C(7,2).
Given: AD/AB = AE/AC = 1/3.
⇒ (AD)/(AD + DB) = 1/3
⇒ 3AD = AD + DB
⇒ 2AD = DB
⇒ AD : DB = 1 : 2.
Also, AE : CE = 1;2
Now,
(i)
Given D divides AB in the ratio 1:2.
Coordinate of D = {1(1) + 2(4)/1+3, 1(5)+2(6)/1+3}
= {3, 17/3}
(ii)
Given E divides AC in the ratio 1:2
Coordinate of E = {1(7)+2(4)/1+3, 1(2)+2(6)/1+3}
= {5,14/3}
We know that Area of triangle = (1/2)[x₁(y₂-y₃)+x₂(y₃-y₂)+x₃(y₂-y₁)]
(iii)
Area of ΔADE = 1/2[4(17/3 - 14/3) + 3(14/3 - 6) + 5(6 - 17/3)]
= 1/2[4 - 4 + 5/3]
= 1/2[5/3]
= 5/6 units.
(iv)
Area of ΔABC = 1/2[4(3) + 1(-4) + 7(1)]
= 1/2[12 - 4 + 7]
= 15/2 units.
(v)
Area of ΔADE/Area of ΔABC = 5/6 * 2/15
= 1/9
Area of ΔADE = (1/9) * Area of ΔABC.
Hope this helps!
Step-by-step explanation:
vertices are A(4,6), B(1,5) and C(7,2).
AD/AB = AE/AC = 1/3.
(AD)/(AD + DB) = 1/3
3AD = AD + DB
2AD = DB
AD : DB = 1 : 2.
Also, AE : CE = 1;2
Now,
Given D divides AB in the ratio 1:2.
Coordinate of D = {1(1) + 2(4)/1+3, 1(5)+2(6)/1+3}
= {3, 17/3}
Given E divides AC in the ratio 1:2
Coordinate of E = {1(7)+2(4)/1+3, 1(2)+2(6)/1+3}
= {5,14/3}
Area of ΔADE = 1/2[4(17/3 - 14/3) + 3(14/3 - 6) + 5(6 - 17/3)]
= 1/2[4 - 4 + 5/3]
= 1/2[5/3]
= 5/6 units.
Area of ΔABC = 1/2[4(3) + 1(-4) + 7(1)]
= 1/2[12 - 4 + 7]
= 15/2 units.
Area of ΔADE/Area of ΔABC = 5/6 * 2/15
= 1/9
Area of ΔADE = (1/9) * Area of ΔABC