D(7,9) , E(1,1) and F(-1,-7) are the vertices of the triangle DEF L(4,5) , M(-1,-3) , and N(2,1) - Maths - Coordinate Geometry

Question

D(7,9) , E(1,1) and F(-1,-7) are the vertices of the triangle
DEF L(4,5) , M(-1,-3) , and N(2,1) are the mid points of DE , EF
and FD respectively prove that
area of triangle DEF/ area of triangle LMN =4/1

Priyanka Kedia · Accepted Answer

Area of
ΔDEF=127×1+1×-7+-1×9-9×1+1×-1+-7×7
=127-7-9-9-1-49 =12-9+41 =8And,Area of
ΔLMN=124×-3+-1×1+2×5-5×-1+-3×2+1×4
=12-12-1+10--5-6+4 =12-3+7 =2Thus,Area of ΔDEFArea of
ΔLMN=82=41Hence proved

D(7,9) , E(1,1) and F(-1,-7) are the vertices of the triangle DEF . L(4,5) , M(-1,-3) , and N(2,1) are the mid points of DE , EF and FD respectively . prove that area of triangle DEF/ area of triangle LMN =4/1

D(7,9) , E(1,1) and F(-1,-7) are the vertices of the triangle DEF . L(4,5) , M(-1,-3) , and N(2,1) are the mid points of DE , EF and FD respectively . prove that

area of triangle DEF/ area of triangle LMN =4/1