AP EAMCET202022 Sep 2020Evening ShiftMathematicsStraight LinesActual
If M is a point on the line y=x and points P(0,1), Q(2,0) are such that P M+Q M is minimum, the coordinates of M are
Options
- A(0,0)
- B( 13 17 , 13 17 )
- C( 2 3 , 2 3 )
- D( 31 7 , 31 7 )
Correct answer
C. ( 2 3 , 2 3 )
Step-by-step solution
Given, aligned & P=(0,1) & Q=(2,0) aligned Let M=(a, a) [ M lies on the line y=x] In order to Make P M+Q M is minimum P, M, Q Must be collinear Slope of P M= Slope of Q M aligned & a-1 a-0 = a-0 a-2 &(a-1)(a-2)=a^2 & a^2-3 a+2=a^2 &-3 a=-2 & a= 2 3 & M is ( 2 3 , 2 3 ) aligned