Question

determine the area of the triangle mno whose midpoints of the sides mn,no and om are p(2,-1)q(4,2) and r(1,4) respectively.
opt A 42 sq units,
B 6 sq units
c 2sq units
d 54 sq units

Answer 1

Answer:

B. 6 sweet units

Step-by-step explanation:

Answer 2

Given the coordinates of midpoints of the sides of a triangle, Find its area.

Explanation:

• The triangle formed by joining the mid-points of the sides of a given bigger triangle divides the area of the bigger triangle into four parts.
• Hence, let the bigger triangle be ABC and the mid points of its each side be M, P, Q. Then the relation between areas of the triangle MPQ and ABC is given by, $ar(\Delta ABC)={4}( ar(\Delta MPQ))$  ----(a)
• Hence, given the coordinates of midpoints p, q, r we get the area of triangle PQR as ,      
•  $ar(PQR)=\frac{1}{2}|2(2-4)+4(4+1)+1(-1-2)| \\ar(PQR)=\frac{1}{2}|-4+20-3|\\ ar(PQR)=\frac{13}{2} \ sq.units$
• From (a) we get the area of triangle MNO as, $ar(MNO)=4(ar(PQR))=26\ sq.units$  ---->ANSWER