Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202317 May 2023Morning ShiftMathematicsStraight LinesActual

If the y -intercept of the perpendicular bisector of the line segment joining P (1,4) and Q ( k , 3) is -4 , then a possible value of k is

Options

  1. A2
  2. B-2
  3. C-4
  4. D1

Correct answer

C. -4

Step-by-step solution

Mid point of P Q is M= ( 1+k 2 ; 7 2 ) Slope of line P Q m= 4-3 1-k = 1 1-k Slope of perpendicular bisector is m m^ =-1 m^ =(k-1) The equation of perpendicular bisector is aligned & (y- 7 2 )=m^ (x- 1+k 2 ) & y=(k-1) (x- 1+k 2 )+ 7 2 aligned Now, for y -intercept of perpendicular bisector: aligned & x=0 & y=(k-1) (0- 1+k 2 )+ 7 2 & y=- (k-1)(1+k) 2 + 7 2 & -4= - (k^2-1 ) 2 + 7 2 & k^2=16 k=4,-4 & k=-4 aligned

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are (1,2) and (4,5) , is 2025The coordinate axes are rotated about the origin in the counter clockwise direction through an angle 60^ . If a and b are the intercepts made on the new axes by a straight line who 2025The image of a point (2,-1) with respect to the line x-y+1=0 is 2025If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle 4 with the negative X -axis in the negative directi 2025A straight line passing through the origin O meets the parallel lines 4 x+2 y=9 and 2 x + y +6=0 at the points P and Q respectively. Then the point O divides the line segment PQ in 2025A (4,3), B (2,5) are two points. If P is a variable point on the same side as that of the origin with respect to the line AB and is at most at a distance of 5 units from the midpoi 2025By shifting the origin to the point (2,3) through translation of axes, if the equation of the curve x^2+3 x y-2 y^2+4 x-y-20=0 is transformed to the form Ax ^2+ Bxy + Cy ^2+ Dx + E 2025The points (2,3) and (-4,- 4 3 ) lie on the opposite sides of the line L 5 x -6 y + k =0 and k is an integer. If the points (1,2) and (4,5) lie on the same side of the line L =0 , 2025 Full Straight Lines list All AP EAMCET PYQs