Question

10. If AB = x +
3, BC = 2x and
AC = 4x - 5,
then for what
value of 'x', B
lies on AC?
*
O a) 2
Ob) 3
O c) 5
d) 8
​

Answer 1

Answer:

Step-by-step explanation:

We then rotate BM by a fixed angle from B,  α  that generates C (i.e. BC is the rotation of BM by a fixed angle)

xC=xMcosα−yMsinα=2cosαcosθ−(2sinθ−b)sinα  

=2cosθcosα−2sinθsinα+bsinα  

yC=xMsinα+yMcosα=2sinαcosθ+(2sinθ−b)cosα  

=2cosθsinα+2sinθcosα−bcosα  

Substituting  cosα=a4andsinα=b4 , this simplifies to

xC=acosα2+bsinα2  

yC=asinα2−bcosα2  

Multiplying both equations by  cosα  then  sinα  allows us to evaluate:

a2=xcosα−ysinα  

b2=xsinα−ycosα  

Squaring both equations and adding:

a2+b24=x2−4xysinαcosα+y2  

x2−2xysin(2α)+y2=4  with  α=0.817  radians