Question

The value of 3 sin (rc/5 - 0) + 4 sin (31/10+ 0) lies in (a) (0, 7] (b) (-7, 7] (c) (-7,0]​

Answer 1

Let AD be the median through the vertex A of△ABC. Then, D is the mid-point of BC. So, the coordinates of D are( 2 −3−1 , 2−2+8 )i.e.,(−2,3).∴AD= (5+2) 2 (−1−3) 2 = 49+16 = 65 units

Let G be the centroid of △ABC. Then, G lies on median AD and divides it in the ratio 2:1. So, coordinates of G are( 2+12×−2+1×5 , 2+12×3+1×−1 )=( 3−4+5 , 36−1 )=( 31 , 35 )