Question

the coordinates of midpoint of the sides of triangle is (3,6),(4,5) and (2,1) , then area of triangle is?




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Answer 1

Answer:

Given : Mid points of a ∆

A. B. C.

(3,6). ( 4,5). (2,1 ).

x1y1. x2y2. x3y3

ar. ∆ ABC = 1/2 ( x1 ( y2-y3) + x2( y3-y1) + x3 ( y1-y2) )

1/2 ( 3(5-1) + 4 (1-6 ) + 2(6-5) )

1/2 ( 3×4 + 4× ( -5) + 2 ×1 )

1/2 ( 12-20+2 )

1/2 ( 14 - 20)

1/2 ( -6 )

= -3

NOTE : area of ∆ can never be negative ....hence ar. ∆ABC is 3 sq. Units

we know that ,

the ratio of ar of ∆ formed by the mid points of original ∆ is always 1:4

let the original Triangle be ∆ PQR

so,

area ∆ ABC 1

____________ = ______

area ∆ PQR 4

3/x = 1/4

x = 3 × 4

x = 12 sq. Units

Hope it helps

Answer 2

Step-by-step explanation:

answer is 12 squre units