Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20228 Jul 2022Morning ShiftMathematicsStraight LinesActual

Given two points Q(3,4) and R(1,2) . What is the point P ( x , y ) on the line 2 x - y -1=0 for which PQ + PR = QR holds

Options

  1. A(-3,-7)
  2. B(-2,-5)
  3. C(2,3)
  4. D(4,7)

Correct answer

C. (2,3)

Step-by-step solution

We are given that PQ + PB = QR aligned & ( x -3)^2+( y -4)^2 + ( x -1)^2+( y -2)^2 & = (3-1)^2+(4-7)^2 & ( x -3)^2+( y -4)^2 + ( x -1)^2+( y -2)^2 = 4+4 & ( x -3)^2+( y -4)^2 + ( x -1)^2+( y -2)^2 = 8 & (2-3)^2+(3-4)^2 + (2-1)^2+(3-2)^2 & 1+1 + 1+1 =2 2 = 8 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