    Question

# For △ABC whose vertices are given by A(3,6),B(−4,7) and C(10,−7), if A1,B1,C1 represent the mid points of sides opposite to vertices A,B,C respectively, of △ABC and A2,B2,C2 represent the mid points of sides opposite to vertices A1,B1,C1 respectively, of △A1B1C1 and so on, then which of the following is/are correct?

A
Area (A2B2C2)Area (ABC)=116
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
Area (A3B3C3)Area (ABC)=116
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
The centroid of A3B3C3 is (3,2)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
The centroid of A2B2C2 is (3,2)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D The centroid of △A2B2C2 is (3,2)Given vertices of △ABC are A(3,6),B(−4,7) and C(10,−7) We know that, Centroid of triangle = Centroid of triangle formed by midpoints. So, centroid of triangles △ABC=△A1B1C1=△A2B2C2…=(3−4+103,6+7−73)=(3,2) Area of triangle formed by midpoints =14×Area of original triangle. So, Area (△A2B2C2)Area (△A1B1C1)=14 and Area (△A1B1C1)Area (△ABC)=14 ∴Area (△A2B2C2)Area (△ABC)=116 Similarly, Area (△A3B3C3)Area (△ABC)=164  Suggest Corrections  0      Similar questions  Related Videos   Basic Concepts
MATHEMATICS
Watch in App  Explore more